A list of Succesful Recurrences or Oder<=, 6, for the Infinite Families of Pisot Sequence with parameter, 1/2 with initial conditions x, x^2*k+y, for x from 2 to , 20, and y from 1 to x^2-1 that is not a multiple of x For GENERAL (symbolic!) k By Shalosh B. Ekhad The Pisot Sequence a(n)=PS(x,y)(n), is defined by, a(1) = x, a(2) = y, 2 a(n + 1) and for n>1, a(n + 2) = trunc(1/2 + ---------) a(n) In this gripping article, we will list PROVED recurrences for the Pisot Seq\ uenes 2 PISOT(x, k x + y) for all (numeric) integers x between 2 and, 20, and all numeric integers, y, that are not divisible by x from 1 to x^2-1. We will use the convention that a linear recurrence of order r a[n]=C1*a[n-1]+ ... +Cr*a[n-r] is abbreviated as a pair of lists: [[a[1], ..., a[r]],[C1, ..., Cr]], where \ the first list consists of the r initial values . {\it PISOT} \left( 2,4\,k+1 \right) =[[2,4\,k+1],[1+2\,k,-k]] {\it PISOT} \left( 2,4\,k+3 \right) =[[2,4\,k+3],[1+2\,k,1+k]] {\it PISOT} \left( 3,9\,k+1 \right) =[[3,9\,k+1],[3\,k,k]] {\it PISOT} \left( 3,9\,k+2 \right) =[[3,9\,k+2,27\,{k}^{2}+12\,k+1],[3 \,k,2\,k,k]] {\it PISOT} \left( 3,9\,k+4 \right) =[[3,9\,k+4],[2+3\,k,-1-2\,k]] {\it PISOT} \left( 3,9\,k+5 \right) =[[3,9\,k+5],[1+3\,k,1+2\,k]] {\it PISOT} \left( 3,9\,k+7 \right) =[[3,9\,k+7,27\,{k}^{2}+42\,k+16],[ 3+3\,k,-2-2\,k,1+k]] {\it PISOT} \left( 3,9\,k+8 \right) =[[3,9\,k+8],[3+3\,k,-1-k]] {\it PISOT} \left( 4,16\,k+1 \right) =[[4,16\,k+1],[4\,k,k]] {\it PISOT} \left( 4,16\,k+2 \right) =[[4,16\,k+2,64\,{k}^{2}+16\,k+1], [1+4\,k,-2\,k,-k]] {\it PISOT} \left( 4,16\,k+5 \right) =[[4,16\,k+5],[2+4\,k,-1-3\,k]] {\it PISOT} \left( 4,16\,k+7 \right) =[[4,16\,k+7,64\,{k}^{2}+56\,k+12] ,[2+4\,k,-1-k,1+2\,k]] {\it PISOT} \left( 4,16\,k+9 \right) =[[4,16\,k+9,64\,{k}^{2}+72\,k+20] ,[2+4\,k,k,1+2\,k]] {\it PISOT} \left( 4,16\,k+10 \right) =[[4,16\,k+10,64\,{k}^{2}+80\,k+ 25],[3+4\,k,-2-2\,k,2+3\,k]] {\it PISOT} \left( 4,16\,k+11 \right) =[[4,16\,k+11],[2+4\,k,2+3\,k]] {\it PISOT} \left( 4,16\,k+14 \right) =[[4,16\,k+14,64\,{k}^{2}+112\,k+ 49],[4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 4,16\,k+15 \right) =[[4,16\,k+15],[4+4\,k,-1-k]] {\it PISOT} \left( 5,25\,k+1 \right) =[[5,25\,k+1],[5\,k,k]] {\it PISOT} \left( 5,25\,k+2 \right) =[[5,25\,k+2,125\,{k}^{2}+20\,k+1] ,[5\,k,2\,k,k]] {\it PISOT} \left( 5,25\,k+3 \right) =[[5,25\,k+3,125\,{k}^{2}+30\,k+2, 625\,{k}^{3}+225\,{k}^{2}+29\,k+1],[5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 5,25\,k+6 \right) =[[5,25\,k+6],[2+5\,k,-1-4\,k]] {\it PISOT} \left( 5,25\,k+8 \right) =[[5,25\,k+8],[1+5\,k,1+3\,k]] {\it PISOT} \left( 5,25\,k+9 \right) =[[5,25\,k+9,125\,{k}^{2}+90\,k+16 ],[2+5\,k,-1-k,1+3\,k]] {\it PISOT} \left( 5,25\,k+11 \right) =[[5,25\,k+11,125\,{k}^{2}+110\,k +24,625\,{k}^{3}+825\,{k}^{2}+361\,k+52],[3+5\,k,-2-4\,k,k,1+2\,k]] {\it PISOT} \left( 5,25\,k+12 \right) =[[5,25\,k+12],[2+5\,k,1+2\,k]] {\it PISOT} \left( 5,25\,k+13 \right) =[[5,25\,k+13],[3+5\,k,-1-2\,k]] {\it PISOT} \left( 5,25\,k+14 \right) =[[5,25\,k+14,125\,{k}^{2}+140\,k +39,625\,{k}^{3}+1050\,{k}^{2}+586\,k+109],[2+5\,k,2+4\,k,1+k,-1-2\,k]] {\it PISOT} \left( 5,25\,k+16 \right) =[[5,25\,k+16,125\,{k}^{2}+160\,k +51],[3+5\,k,k,2+3\,k]] {\it PISOT} \left( 5,25\,k+17 \right) =[[5,25\,k+17],[4+5\,k,-2-3\,k]] {\it PISOT} \left( 5,25\,k+19 \right) =[[5,25\,k+19],[3+5\,k,3+4\,k]] {\it PISOT} \left( 5,25\,k+22 \right) =[[5,25\,k+22,125\,{k}^{2}+220\,k +97,625\,{k}^{3}+1650\,{k}^{2}+1454\,k+428],[5+5\,k,-3-3\,k,2+2\,k,-1-k ]] {\it PISOT} \left( 5,25\,k+23 \right) =[[5,25\,k+23,125\,{k}^{2}+230\,k +106],[5+5\,k,-2-2\,k,1+k]] {\it PISOT} \left( 5,25\,k+24 \right) =[[5,25\,k+24],[5+5\,k,-1-k]] {\it PISOT} \left( 6,36\,k+1 \right) =[[6,36\,k+1],[6\,k,k]] {\it PISOT} \left( 6,36\,k+2 \right) =[[6,36\,k+2,216\,{k}^{2}+24\,k+1] ,[6\,k,2\,k,k]] {\it PISOT} \left( 6,36\,k+3 \right) =[[6,36\,k+3,216\,{k}^{2}+36\,k+2, 1296\,{k}^{3}+324\,{k}^{2}+33\,k+1],[1+6\,k,-3\,k,-k,-k]] {\it PISOT} \left( 6,36\,k+4 \right) =[[6,36\,k+4,216\,{k}^{2}+48\,k+3, 1296\,{k}^{3}+432\,{k}^{2}+52\,k+2,7776\,{k}^{4}+3456\,{k}^{3}+612\,{k} ^{2}+48\,k+1],[6\,k,4\,k,3\,k,2\,k,k]] {\it PISOT} \left( 6,36\,k+7 \right) =[[6,36\,k+7],[2+6\,k,-1-5\,k]] {\it PISOT} \left( 6,36\,k+8 \right) =[[6,36\,k+8,216\,{k}^{2}+96\,k+11 ,1296\,{k}^{3}+864\,{k}^{2}+196\,k+15],[1+6\,k,1+2\,k,-3\,k,-1-4\,k]] {\it PISOT} \left( 6,36\,k+11 \right) =[[6,36\,k+11,216\,{k}^{2}+132\,k +20,1296\,{k}^{3}+1188\,{k}^{2}+361\,k+36,7776\,{k}^{4}+9504\,{k}^{3}+ 4338\,{k}^{2}+872\,k+65,46656\,{k}^{5}+71280\,{k}^{4}+43416\,{k}^{3}+ 13139\,{k}^{2}+1972\,k+117],[2+6\,k,-1-k,1+4\,k,k,2\,k,1+3\,k]] {\it PISOT} \left( 6,36\,k+13 \right) =[[6,36\,k+13,216\,{k}^{2}+156\,k +28],[1+6\,k,2+7\,k,1+3\,k]] {\it PISOT} \left( 6,36\,k+14 \right) =[[6,36\,k+14,216\,{k}^{2}+168\,k +33],[2+6\,k,2\,k,2+5\,k]] {\it PISOT} \left( 6,36\,k+15 \right) =[[6,36\,k+15,216\,{k}^{2}+180\,k +38,1296\,{k}^{3}+1620\,{k}^{2}+681\,k+96,7776\,{k}^{4}+12960\,{k}^{3}+ 8154\,{k}^{2}+2292\,k+243],[3+6\,k,-1-3\,k,-k,-2-3\,k,2+5\,k]] No uniform order {\it PISOT} \left( 6,36\,k+17 \right) =[[6,36\,k+17,216\,{k}^{2}+204\,k +48],[2+6\,k,2+5\,k,1+2\,k]] {\it PISOT} \left( 6,36\,k+19 \right) =[[6,36\,k+19,216\,{k}^{2}+228\,k +60],[4+6\,k,-3-5\,k,1+2\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.997933255553849 {\it PISOT} \left( 6,36\,k+20 \right) =[[6,36\,k+20,216\,{k}^{2}+240\,k +67,1296\,{k}^{3}+2160\,{k}^{2}+1204\,k+224,7776\,{k}^{4}+17280\,{k}^{3 }+14436\,{k}^{2}+5368\,k+749],[3+6\,k,1+2\,k,1+k,-2-3\,k,1+2\,k]] No uniform order {\it PISOT} \left( 6,36\,k+22 \right) =[[6,36\,k+22,216\,{k}^{2}+264\,k +81],[4+6\,k,-2-2\,k,3+5\,k]] {\it PISOT} \left( 6,36\,k+23 \right) =[[6,36\,k+23,216\,{k}^{2}+276\,k +88],[5+6\,k,-5-7\,k,2+3\,k]] {\it PISOT} \left( 6,36\,k+25 \right) =[[6,36\,k+25,216\,{k}^{2}+300\,k +104,1296\,{k}^{3}+2700\,{k}^{2}+1873\,k+433,7776\,{k}^{4}+21600\,{k}^{ 3}+22482\,{k}^{2}+10396\,k+1803,46656\,{k}^{5}+162000\,{k}^{4}+224856\, {k}^{3}+155989\,{k}^{2}+54102\,k+7508],[4+6\,k,k,3+4\,k,-1-k,2+2\,k,-2- 3\,k]] {\it PISOT} \left( 6,36\,k+28 \right) =[[6,36\,k+28,216\,{k}^{2}+336\,k +131,1296\,{k}^{3}+3024\,{k}^{2}+2356\,k+613],[5+6\,k,-1-2\,k,-3-3\,k,3 +4\,k]] {\it PISOT} \left( 6,36\,k+29 \right) =[[6,36\,k+29],[4+6\,k,4+5\,k]] {\it PISOT} \left( 6,36\,k+32 \right) =[[6,36\,k+32,216\,{k}^{2}+384\,k +171,1296\,{k}^{3}+3456\,{k}^{2}+3076\,k+914,7776\,{k}^{4}+27648\,{k}^{ 3}+36900\,{k}^{2}+21912\,k+4885],[6+6\,k,-4-4\,k,3+3\,k,-2-2\,k,1+k]] {\it PISOT} \left( 6,36\,k+33 \right) =[[6,36\,k+33,216\,{k}^{2}+396\,k +182,1296\,{k}^{3}+3564\,{k}^{2}+3273\,k+1004],[5+6\,k,3+3\,k,-1-k,1+k] ] {\it PISOT} \left( 6,36\,k+34 \right) =[[6,36\,k+34,216\,{k}^{2}+408\,k +193],[6+6\,k,-2-2\,k,1+k]] {\it PISOT} \left( 6,36\,k+35 \right) =[[6,36\,k+35],[6+6\,k,-1-k]] {\it PISOT} \left( 7,49\,k+1 \right) =[[7,49\,k+1],[7\,k,k]] {\it PISOT} \left( 7,49\,k+2 \right) =[[7,49\,k+2,343\,{k}^{2}+28\,k+1] ,[7\,k,2\,k,k]] {\it PISOT} \left( 7,49\,k+3 \right) =[[7,49\,k+3,343\,{k}^{2}+42\,k+1] ,[7\,k,3\,k,k]] {\it PISOT} \left( 7,49\,k+4 \right) =[[7,49\,k+4,343\,{k}^{2}+56\,k+2, 2401\,{k}^{3}+588\,{k}^{2}+44\,k+1],[1+7\,k,-3\,k,-2\,k,-k]] {\it PISOT} \left( 7,49\,k+8 \right) =[[7,49\,k+8],[2+7\,k,-1-6\,k]] {\it PISOT} \left( 7,49\,k+9 \right) =[[7,49\,k+9,343\,{k}^{2}+126\,k+ 12],[7\,k,1+9\,k,1+5\,k]] {\it PISOT} \left( 7,49\,k+12 \right) =[[7,49\,k+12,343\,{k}^{2}+168\,k +21],[2+7\,k,-1-2\,k,1+4\,k]] {\it PISOT} \left( 7,49\,k+13 \right) =[[7,49\,k+13,343\,{k}^{2}+182\,k +24],[1+7\,k,1+6\,k,1+4\,k]] {\it PISOT} \left( 7,49\,k+15 \right) =[[7,49\,k+15,343\,{k}^{2}+210\,k +32,2401\,{k}^{3}+2205\,{k}^{2}+673\,k+68],[2+7\,k,k,1+2\,k,-1-3\,k]] {\it PISOT} \left( 7,49\,k+16 \right) =[[7,49\,k+16,343\,{k}^{2}+224\,k +37],[3+7\,k,-2-5\,k,1+3\,k]] {\it PISOT} \left( 7,49\,k+17 \right) =[[7,49\,k+17],[2+7\,k,1+3\,k]] {\it PISOT} \left( 7,49\,k+18 \right) =[[7,49\,k+18,343\,{k}^{2}+252\,k +46,2401\,{k}^{3}+2646\,{k}^{2}+968\,k+118],[2+7\,k,2+4\,k,-1-4\,k,-1-3 \,k]] {\it PISOT} \left( 7,49\,k+19 \right) =[[7,49\,k+19],[2+7\,k,2+5\,k]] {\it PISOT} \left( 7,49\,k+20 \right) =[[7,49\,k+20,343\,{k}^{2}+280\,k +57],[4+7\,k,-4-8\,k,2+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.993167813742437 {\it PISOT} \left( 7,49\,k+22 \right) =[[7,49\,k+22,343\,{k}^{2}+308\,k +69,2401\,{k}^{3}+3234\,{k}^{2}+1450\,k+216],[2+7\,k,3+8\,k,2+4\,k,-1-2 \,k]] {\it PISOT} \left( 7,49\,k+23 \right) =[[7,49\,k+23],[3+7\,k,1+2\,k]] {\it PISOT} \left( 7,49\,k+24 \right) =[[7,49\,k+24],[4+7\,k,-2-4\,k]] {\it PISOT} \left( 7,49\,k+25 \right) =[[7,49\,k+25],[3+7\,k,2+4\,k]] {\it PISOT} \left( 7,49\,k+26 \right) =[[7,49\,k+26],[4+7\,k,-1-2\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.993159161676151 {\it PISOT} \left( 7,49\,k+27 \right) =[[7,49\,k+27,343\,{k}^{2}+378\,k +104,2401\,{k}^{3}+3969\,{k}^{2}+2185\,k+401],[5+7\,k,-5-8\,k,2+4\,k,1+ 2\,k]] {\it PISOT} \left( 7,49\,k+29 \right) =[[7,49\,k+29,343\,{k}^{2}+406\,k +120],[3+7\,k,4+8\,k,3+5\,k]] {\it PISOT} \left( 7,49\,k+30 \right) =[[7,49\,k+30],[5+7\,k,-3-5\,k]] {\it PISOT} \left( 7,49\,k+31 \right) =[[7,49\,k+31,343\,{k}^{2}+434\,k +137,2401\,{k}^{3}+4557\,{k}^{2}+2879\,k+605],[5+7\,k,-2-4\,k,-3-4\,k,2 +3\,k]] {\it PISOT} \left( 7,49\,k+32 \right) =[[7,49\,k+32],[5+7\,k,-2-3\,k]] {\it PISOT} \left( 7,49\,k+33 \right) =[[7,49\,k+33,343\,{k}^{2}+462\,k +156],[4+7\,k,3+5\,k,2+3\,k]] {\it PISOT} \left( 7,49\,k+34 \right) =[[7,49\,k+34,343\,{k}^{2}+476\,k +165,2401\,{k}^{3}+4998\,{k}^{2}+3466\,k+801],[5+7\,k,-1-k,1+2\,k,2+3\, k]] {\it PISOT} \left( 7,49\,k+36 \right) =[[7,49\,k+36,343\,{k}^{2}+504\,k +185],[6+7\,k,-5-6\,k,3+4\,k]] {\it PISOT} \left( 7,49\,k+37 \right) =[[7,49\,k+37,343\,{k}^{2}+518\,k +196],[5+7\,k,1+2\,k,3+4\,k]] {\it PISOT} \left( 7,49\,k+40 \right) =[[7,49\,k+40,343\,{k}^{2}+560\,k +229],[7+7\,k,-8-9\,k,4+5\,k]] {\it PISOT} \left( 7,49\,k+41 \right) =[[7,49\,k+41],[5+7\,k,5+6\,k]] {\it PISOT} \left( 7,49\,k+45 \right) =[[7,49\,k+45,343\,{k}^{2}+630\,k +289,2401\,{k}^{3}+6615\,{k}^{2}+6071\,k+1856],[6+7\,k,3+3\,k,-2-2\,k,1 +k]] {\it PISOT} \left( 7,49\,k+46 \right) =[[7,49\,k+46,343\,{k}^{2}+644\,k +302],[7+7\,k,-3-3\,k,1+k]] {\it PISOT} \left( 7,49\,k+47 \right) =[[7,49\,k+47,343\,{k}^{2}+658\,k +316],[7+7\,k,-2-2\,k,1+k]] {\it PISOT} \left( 7,49\,k+48 \right) =[[7,49\,k+48],[7+7\,k,-1-k]] {\it PISOT} \left( 8,64\,k+1 \right) =[[8,64\,k+1],[8\,k,k]] {\it PISOT} \left( 8,64\,k+2 \right) =[[8,64\,k+2,512\,{k}^{2}+32\,k+1] ,[8\,k,2\,k,k]] {\it PISOT} \left( 8,64\,k+3 \right) =[[8,64\,k+3,512\,{k}^{2}+48\,k+1] ,[8\,k,3\,k,k]] {\it PISOT} \left( 8,64\,k+4 \right) =[[8,64\,k+4,512\,{k}^{2}+64\,k+2, 4096\,{k}^{3}+768\,{k}^{2}+48\,k+1],[1+8\,k,-4\,k,-2\,k,-k]] {\it PISOT} \left( 8,64\,k+5 \right) =[[8,64\,k+5,512\,{k}^{2}+80\,k+3, 4096\,{k}^{3}+960\,{k}^{2}+73\,k+2,32768\,{k}^{4}+10240\,{k}^{3}+1176\, {k}^{2}+62\,k+1],[8\,k,5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 8,64\,k+9 \right) =[[8,64\,k+9],[2+8\,k,-1-7\,k]] {\it PISOT} \left( 8,64\,k+11 \right) =[[8,64\,k+11,512\,{k}^{2}+176\,k +15,4096\,{k}^{3}+2112\,{k}^{2}+361\,k+20],[1+8\,k,1+3\,k,-4\,k,-1-6\,k ]] {\it PISOT} \left( 8,64\,k+13 \right) =[[8,64\,k+13],[1+8\,k,1+5\,k]] {\it PISOT} \left( 8,64\,k+15 \right) =[[8,64\,k+15,512\,{k}^{2}+240\,k +28,4096\,{k}^{3}+2880\,{k}^{2}+673\,k+52],[2+8\,k,-k,-1-2\,k,1+4\,k]] {\it PISOT} \left( 8,64\,k+17 \right) =[[8,64\,k+17,512\,{k}^{2}+272\,k +36,4096\,{k}^{3}+3264\,{k}^{2}+865\,k+76],[2+8\,k,k,2\,k,1+4\,k]] {\it PISOT} \left( 8,64\,k+18 \right) =[[8,64\,k+18,512\,{k}^{2}+288\,k +41],[1+8\,k,2+10\,k,2+7\,k]] {\it PISOT} \left( 8,64\,k+20 \right) =[[8,64\,k+20,512\,{k}^{2}+320\,k +50,4096\,{k}^{3}+3840\,{k}^{2}+1200\,k+125],[3+8\,k,-1-4\,k,-1-2\,k,1+ 3\,k]] {\it PISOT} \left( 8,64\,k+21 \right) =[[8,64\,k+21],[3+8\,k,-1-3\,k]] {\it PISOT} \left( 8,64\,k+22 \right) =[[8,64\,k+22,512\,{k}^{2}+352\,k +61],[3+8\,k,-1-2\,k,1+3\,k]] {\it PISOT} \left( 8,64\,k+23 \right) =[[8,64\,k+23,512\,{k}^{2}+368\,k +66,4096\,{k}^{3}+4416\,{k}^{2}+1585\,k+189],[2+8\,k,2+7\,k,1+4\,k,1+3 \,k]] {\it PISOT} \left( 8,64\,k+25 \right) =[[8,64\,k+25,512\,{k}^{2}+400\,k +78],[3+8\,k,1+k,-2-5\,k]] {\it PISOT} \left( 8,64\,k+26 \right) =[[8,64\,k+26,512\,{k}^{2}+416\,k +85],[4+8\,k,-3-6\,k,2+5\,k]] {\it PISOT} \left( 8,64\,k+27 \right) =[[8,64\,k+27,512\,{k}^{2}+432\,k +91],[4+8\,k,-3-5\,k,3+7\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.992185566218502 {\it PISOT} \left( 8,64\,k+28 \right) =[[8,64\,k+28,512\,{k}^{2}+448\,k +98,4096\,{k}^{3}+5376\,{k}^{2}+2352\,k+343],[3+8\,k,2+4\,k,-2\,k,-3-7 \,k]] {\it PISOT} \left( 8,64\,k+31 \right) =[[8,64\,k+31,512\,{k}^{2}+496\,k +120],[4+8\,k,-1-k,2+4\,k]] {\it PISOT} \left( 8,64\,k+33 \right) =[[8,64\,k+33,512\,{k}^{2}+528\,k +136],[4+8\,k,k,2+4\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.992191523674274 {\it PISOT} \left( 8,64\,k+36 \right) =[[8,64\,k+36,512\,{k}^{2}+576\,k +162,4096\,{k}^{3}+6912\,{k}^{2}+3888\,k+729],[5+8\,k,-2-4\,k,-2-2\,k,4 +7\,k]] {\it PISOT} \left( 8,64\,k+37 \right) =[[8,64\,k+37,512\,{k}^{2}+592\,k +171],[4+8\,k,2+5\,k,4+7\,k]] {\it PISOT} \left( 8,64\,k+38 \right) =[[8,64\,k+38,512\,{k}^{2}+608\,k +181],[4+8\,k,3+6\,k,3+5\,k]] {\it PISOT} \left( 8,64\,k+39 \right) =[[8,64\,k+39,512\,{k}^{2}+624\,k +190],[5+8\,k,-k,-3-5\,k]] {\it PISOT} \left( 8,64\,k+41 \right) =[[8,64\,k+41,512\,{k}^{2}+656\,k +210,4096\,{k}^{3}+7872\,{k}^{2}+5041\,k+1076],[6+8\,k,-5-7\,k,3+4\,k,- 2-3\,k]] {\it PISOT} \left( 8,64\,k+42 \right) =[[8,64\,k+42,512\,{k}^{2}+672\,k +221],[5+8\,k,1+2\,k,2+3\,k]] {\it PISOT} \left( 8,64\,k+43 \right) =[[8,64\,k+43],[5+8\,k,2+3\,k]] {\it PISOT} \left( 8,64\,k+44 \right) =[[8,64\,k+44,512\,{k}^{2}+704\,k +242,4096\,{k}^{3}+8448\,{k}^{2}+5808\,k+1331],[5+8\,k,3+4\,k,-1-2\,k,- 2-3\,k]] {\it PISOT} \left( 8,64\,k+46 \right) =[[8,64\,k+46,512\,{k}^{2}+736\,k +265],[7+8\,k,-8-10\,k,5+7\,k]] {\it PISOT} \left( 8,64\,k+47 \right) =[[8,64\,k+47,512\,{k}^{2}+752\,k +276,4096\,{k}^{3}+9024\,{k}^{2}+6625\,k+1621],[6+8\,k,-1-k,2+2\,k,-3-4 \,k]] {\it PISOT} \left( 8,64\,k+49 \right) =[[8,64\,k+49,512\,{k}^{2}+784\,k +300,4096\,{k}^{3}+9408\,{k}^{2}+7201\,k+1837],[6+8\,k,1+k,-1-2\,k,-3-4 \,k]] {\it PISOT} \left( 8,64\,k+51 \right) =[[8,64\,k+51],[7+8\,k,-4-5\,k]] {\it PISOT} \left( 8,64\,k+53 \right) =[[8,64\,k+53,512\,{k}^{2}+848\,k +351,4096\,{k}^{3}+10176\,{k}^{2}+8425\,k+2325],[7+8\,k,-2-3\,k,-4-4\,k ,5+6\,k]] {\it PISOT} \left( 8,64\,k+55 \right) =[[8,64\,k+55],[6+8\,k,6+7\,k]] {\it PISOT} \left( 8,64\,k+59 \right) =[[8,64\,k+59,512\,{k}^{2}+944\,k +435,4096\,{k}^{3}+11328\,{k}^{2}+10441\,k+3207,32768\,{k}^{4}+120832\, {k}^{3}+167064\,{k}^{2}+102642\,k+23643],[8+8\,k,-5-5\,k,3+3\,k,-2-2\,k ,1+k]] {\it PISOT} \left( 8,64\,k+60 \right) =[[8,64\,k+60,512\,{k}^{2}+960\,k +450,4096\,{k}^{3}+11520\,{k}^{2}+10800\,k+3375],[7+8\,k,4+4\,k,-2-2\,k ,1+k]] {\it PISOT} \left( 8,64\,k+61 \right) =[[8,64\,k+61,512\,{k}^{2}+976\,k +465],[8+8\,k,-3-3\,k,1+k]] {\it PISOT} \left( 8,64\,k+62 \right) =[[8,64\,k+62,512\,{k}^{2}+992\,k +481],[8+8\,k,-2-2\,k,1+k]] {\it PISOT} \left( 8,64\,k+63 \right) =[[8,64\,k+63],[8+8\,k,-1-k]] {\it PISOT} \left( 9,81\,k+1 \right) =[[9,81\,k+1],[9\,k,k]] {\it PISOT} \left( 9,81\,k+2 \right) =[[9,81\,k+2],[9\,k,2\,k]] {\it PISOT} \left( 9,81\,k+3 \right) =[[9,81\,k+3,729\,{k}^{2}+54\,k+1] ,[9\,k,3\,k,k]] {\it PISOT} \left( 9,81\,k+4 \right) =[[9,81\,k+4,729\,{k}^{2}+72\,k+2, 6561\,{k}^{3}+972\,{k}^{2}+52\,k+1],[9\,k,4\,k,2\,k,k]] {\it PISOT} \left( 9,81\,k+5 \right) =[[9,81\,k+5,729\,{k}^{2}+90\,k+3, 6561\,{k}^{3}+1215\,{k}^{2}+79\,k+2,59049\,{k}^{4}+14580\,{k}^{3}+1404 \,{k}^{2}+66\,k+1],[1+9\,k,-4\,k,-2\,k,-k,-k]] {\it PISOT} \left( 9,81\,k+6 \right) =[[9,81\,k+6,729\,{k}^{2}+108\,k+4 ,6561\,{k}^{3}+1458\,{k}^{2}+108\,k+3,59049\,{k}^{4}+17496\,{k}^{3}+ 1944\,{k}^{2}+102\,k+2,531441\,{k}^{5}+196830\,{k}^{4}+29160\,{k}^{3}+ 2241\,{k}^{2}+88\,k+1],[9\,k,6\,k,4\,k,3\,k,2\,k,k]] {\it PISOT} \left( 9,81\,k+10 \right) =[[9,81\,k+10],[2+9\,k,-1-8\,k]] {\it PISOT} \left( 9,81\,k+11 \right) =[[9,81\,k+11],[2+9\,k,-1-7\,k]] {\it PISOT} \left( 9,81\,k+12 \right) =[[9,81\,k+12,729\,{k}^{2}+216\,k +16],[9\,k,1+12\,k,1+7\,k]] {\it PISOT} \left( 9,81\,k+13 \right) =[[9,81\,k+13,729\,{k}^{2}+234\,k +19],[1+9\,k,4\,k,1+6\,k]] {\it PISOT} \left( 9,81\,k+16 \right) =[[9,81\,k+16,729\,{k}^{2}+288\,k +28],[2+9\,k,-1-2\,k,1+5\,k]] {\it PISOT} \left( 9,81\,k+17 \right) =[[9,81\,k+17,729\,{k}^{2}+306\,k +32,6561\,{k}^{3}+4131\,{k}^{2}+865\,k+60],[2+9\,k,-k,-1-2\,k,1+5\,k]] {\it PISOT} \left( 9,81\,k+20 \right) =[[9,81\,k+20,729\,{k}^{2}+360\,k +44],[2+9\,k,2\,k,1+4\,k]] {\it PISOT} \left( 9,81\,k+21 \right) =[[9,81\,k+21,729\,{k}^{2}+378\,k +49],[3+9\,k,-2-6\,k,1+4\,k]] {\it PISOT} \left( 9,81\,k+25 \right) =[[9,81\,k+25,729\,{k}^{2}+450\,k +69,6561\,{k}^{3}+6075\,{k}^{2}+1867\,k+190,59049\,{k}^{4}+72900\,{k}^{ 3}+33642\,{k}^{2}+6870\,k+523],[3+9\,k,-2\,k,-2-6\,k,k,1+3\,k]] {\it PISOT} \left( 9,81\,k+26 \right) =[[9,81\,k+26,729\,{k}^{2}+468\,k +75],[3+9\,k,-k,-1-3\,k]] {\it PISOT} \left( 9,81\,k+28 \right) =[[9,81\,k+28,729\,{k}^{2}+504\,k +87],[3+9\,k,k,1+3\,k]] {\it PISOT} \left( 9,81\,k+29 \right) =[[9,81\,k+29,729\,{k}^{2}+522\,k +93,6561\,{k}^{3}+7047\,{k}^{2}+2515\,k+298,59049\,{k}^{4}+84564\,{k}^{ 3}+45306\,{k}^{2}+10758\,k+955],[3+9\,k,2\,k,2+6\,k,k,1+3\,k]] {\it PISOT} \left( 9,81\,k+31 \right) =[[9,81\,k+31,729\,{k}^{2}+558\,k +107,6561\,{k}^{3}+7533\,{k}^{2}+2887\,k+369,59049\,{k}^{4}+90396\,{k}^ {3}+51948\,{k}^{2}+13276\,k+1273],[3+9\,k,2+4\,k,-2-4\,k,1+4\,k,2+5\,k] ] {\it PISOT} \left( 9,81\,k+32 \right) =[[9,81\,k+32],[3+9\,k,2+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.994621911397805 {\it PISOT} \left( 9,81\,k+38 \right) =[[9,81\,k+38,729\,{k}^{2}+684\,k +160,6561\,{k}^{3}+9234\,{k}^{2}+4324\,k+674],[4+9\,k,2\,k,4+8\,k,-1-2 \,k]] {\it PISOT} \left( 9,81\,k+39 \right) =[[9,81\,k+39,729\,{k}^{2}+702\,k +169,6561\,{k}^{3}+9477\,{k}^{2}+4563\,k+732],[5+9\,k,-3-6\,k,k,2+4\,k] ] {\it PISOT} \left( 9,81\,k+40 \right) =[[9,81\,k+40],[4+9\,k,2+4\,k]] {\it PISOT} \left( 9,81\,k+41 \right) =[[9,81\,k+41],[5+9\,k,-2-4\,k]] {\it PISOT} \left( 9,81\,k+42 \right) =[[9,81\,k+42,729\,{k}^{2}+756\,k +196,6561\,{k}^{3}+10206\,{k}^{2}+5292\,k+915],[4+9\,k,3+6\,k,1+k,-2-4 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.994616534533709 {\it PISOT} \left( 9,81\,k+43 \right) =[[9,81\,k+43,729\,{k}^{2}+774\,k +205,6561\,{k}^{3}+10449\,{k}^{2}+5539\,k+977],[5+9\,k,-2-2\,k,4+8\,k,1 +2\,k]] {\it PISOT} \left( 9,81\,k+49 \right) =[[9,81\,k+49],[6+9\,k,-3-5\,k]] {\it PISOT} \left( 9,81\,k+50 \right) =[[9,81\,k+50,729\,{k}^{2}+900\,k +278,6561\,{k}^{3}+12150\,{k}^{2}+7504\,k+1546,59049\,{k}^{4}+145800\,{ k}^{3}+135054\,{k}^{2}+55628\,k+8598],[6+9\,k,-2-4\,k,-2-4\,k,-3-4\,k,3 +5\,k]] {\it PISOT} \left( 9,81\,k+52 \right) =[[9,81\,k+52,729\,{k}^{2}+936\,k +300,6561\,{k}^{3}+12636\,{k}^{2}+8104\,k+1731,59049\,{k}^{4}+151632\,{ k}^{3}+145908\,{k}^{2}+62358\,k+9988],[6+9\,k,-2-2\,k,4+6\,k,-1-k,2+3\, k]] {\it PISOT} \left( 9,81\,k+53 \right) =[[9,81\,k+53,729\,{k}^{2}+954\,k +312],[6+9\,k,-1-k,2+3\,k]] {\it PISOT} \left( 9,81\,k+55 \right) =[[9,81\,k+55,729\,{k}^{2}+990\,k +336],[6+9\,k,1+k,-2-3\,k]] {\it PISOT} \left( 9,81\,k+56 \right) =[[9,81\,k+56,729\,{k}^{2}+1008\, k+348,6561\,{k}^{3}+13608\,{k}^{2}+9400\,k+2163,59049\,{k}^{4}+163296\, {k}^{3}+169236\,{k}^{2}+77910\,k+13444],[6+9\,k,2+2\,k,-4-6\,k,-1-k,2+3 \,k]] {\it PISOT} \left( 9,81\,k+60 \right) =[[9,81\,k+60,729\,{k}^{2}+1080\, k+400],[6+9\,k,4+6\,k,3+4\,k]] {\it PISOT} \left( 9,81\,k+61 \right) =[[9,81\,k+61,729\,{k}^{2}+1098\, k+413],[7+9\,k,-2-2\,k,3+4\,k]] {\it PISOT} \left( 9,81\,k+64 \right) =[[9,81\,k+64,729\,{k}^{2}+1152\, k+455,6561\,{k}^{3}+15552\,{k}^{2}+12286\,k+3235],[7+9\,k,1+k,-1-2\,k,- 4-5\,k]] {\it PISOT} \left( 9,81\,k+65 \right) =[[9,81\,k+65,729\,{k}^{2}+1170\, k+469],[7+9\,k,1+2\,k,4+5\,k]] {\it PISOT} \left( 9,81\,k+68 \right) =[[9,81\,k+68,729\,{k}^{2}+1224\, k+514],[8+9\,k,-4-4\,k,5+6\,k]] {\it PISOT} \left( 9,81\,k+69 \right) =[[9,81\,k+69,729\,{k}^{2}+1242\, k+529],[9+9\,k,-11-12\,k,6+7\,k]] {\it PISOT} \left( 9,81\,k+70 \right) =[[9,81\,k+70],[7+9\,k,6+7\,k]] {\it PISOT} \left( 9,81\,k+71 \right) =[[9,81\,k+71],[7+9\,k,7+8\,k]] {\it PISOT} \left( 9,81\,k+75 \right) =[[9,81\,k+75,729\,{k}^{2}+1350\, k+625,6561\,{k}^{3}+18225\,{k}^{2}+16875\,k+5208,59049\,{k}^{4}+218700 \,{k}^{3}+303750\,{k}^{2}+187494\,k+43397,531441\,{k}^{5}+2460375\,{k}^ {4}+4556250\,{k}^{3}+4218669\,{k}^{2}+1952971\,k+361617],[9+9\,k,-6-6\, k,4+4\,k,-3-3\,k,2+2\,k,-1-k]] {\it PISOT} \left( 9,81\,k+76 \right) =[[9,81\,k+76,729\,{k}^{2}+1368\, k+642,6561\,{k}^{3}+18468\,{k}^{2}+17332\,k+5423,59049\,{k}^{4}+221616 \,{k}^{3}+311958\,{k}^{2}+195198\,k+45808],[8+9\,k,4+4\,k,-2-2\,k,1+k,- 1-k]] {\it PISOT} \left( 9,81\,k+77 \right) =[[9,81\,k+77,729\,{k}^{2}+1386\, k+659,6561\,{k}^{3}+18711\,{k}^{2}+17791\,k+5640],[9+9\,k,-4-4\,k,2+2\, k,-1-k]] {\it PISOT} \left( 9,81\,k+78 \right) =[[9,81\,k+78,729\,{k}^{2}+1404\, k+676],[9+9\,k,-3-3\,k,1+k]] {\it PISOT} \left( 9,81\,k+79 \right) =[[9,81\,k+79],[9+9\,k,-2-2\,k]] {\it PISOT} \left( 9,81\,k+80 \right) =[[9,81\,k+80],[9+9\,k,-1-k]] {\it PISOT} \left( 10,100\,k+1 \right) =[[10,100\,k+1],[10\,k,k]] {\it PISOT} \left( 10,100\,k+2 \right) =[[10,100\,k+2],[10\,k,2\,k]] {\it PISOT} \left( 10,100\,k+3 \right) =[[10,100\,k+3,1000\,{k}^{2}+60 \,k+1],[10\,k,3\,k,k]] {\it PISOT} \left( 10,100\,k+4 \right) =[[10,100\,k+4,1000\,{k}^{2}+80 \,k+2,10000\,{k}^{3}+1200\,{k}^{2}+56\,k+1],[10\,k,4\,k,2\,k,k]] {\it PISOT} \left( 10,100\,k+5 \right) =[[10,100\,k+5,1000\,{k}^{2}+100 \,k+3,10000\,{k}^{3}+1500\,{k}^{2}+85\,k+2,100000\,{k}^{4}+20000\,{k}^{ 3}+1650\,{k}^{2}+70\,k+1],[1+10\,k,-5\,k,-2\,k,-k,-k]] {\it PISOT} \left( 10,100\,k+11 \right) =[[10,100\,k+11],[2+10\,k,-1-9 \,k]] {\it PISOT} \left( 10,100\,k+12 \right) =[[10,100\,k+12],[2+10\,k,-1-8 \,k]] {\it PISOT} \left( 10,100\,k+16 \right) =[[10,100\,k+16],[1+10\,k,1+6\, k]] {\it PISOT} \left( 10,100\,k+24 \right) =[[10,100\,k+24],[2+10\,k,1+4\, k]] {\it PISOT} \left( 10,100\,k+25 \right) =[[10,100\,k+25,1000\,{k}^{2}+ 500\,k+63],[3+10\,k,-2-5\,k,2+8\,k]] {\it PISOT} \left( 10,100\,k+26 \right) =[[10,100\,k+26],[3+10\,k,-1-4 \,k]] {\it PISOT} \left( 10,100\,k+29 \right) =[[10,100\,k+29,1000\,{k}^{2}+ 580\,k+84],[3+10\,k,-1-k,2+7\,k]] {\it PISOT} \left( 10,100\,k+32 \right) =[[10,100\,k+32,1000\,{k}^{2}+ 640\,k+102,10000\,{k}^{3}+9600\,{k}^{2}+3064\,k+325,100000\,{k}^{4}+ 128000\,{k}^{3}+61320\,{k}^{2}+13028\,k+1036],[3+10\,k,2\,k,2+6\,k,-k,- 1-3\,k]] {\it PISOT} \left( 10,100\,k+33 \right) =[[10,100\,k+33],[3+10\,k,1+3\, k]] {\it PISOT} \left( 10,100\,k+34 \right) =[[10,100\,k+34],[4+10\,k,-2-6 \,k]] {\it PISOT} \left( 10,100\,k+35 \right) =[[10,100\,k+35,1000\,{k}^{2}+ 700\,k+123],[4+10\,k,-2-5\,k,1+3\,k]] {\it PISOT} \left( 10,100\,k+38 \right) =[[10,100\,k+38],[3+10\,k,3+8\, k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.982594394352120 {\it PISOT} \left( 10,100\,k+39 \right) =[[10,100\,k+39,1000\,{k}^{2}+ 780\,k+152,10000\,{k}^{3}+11700\,{k}^{2}+4561\,k+592,100000\,{k}^{4}+ 156000\,{k}^{3}+91230\,{k}^{2}+23696\,k+2306,1000000\,{k}^{5}+1950000\, {k}^{4}+1520600\,{k}^{3}+592599\,{k}^{2}+115400\,k+8982],[5+10\,k,-5-11 \,k,3+7\,k,-1-3\,k,-1-k,2+5\,k]] {\it PISOT} \left( 10,100\,k+41 \right) =[[10,100\,k+41,1000\,{k}^{2}+ 820\,k+168],[3+10\,k,4+11\,k,2+5\,k]] {\it PISOT} \left( 10,100\,k+43 \right) =[[10,100\,k+43],[5+10\,k,-3-7 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.972273917844570 {\it PISOT} \left( 10,100\,k+45 \right) =[[10,100\,k+45,1000\,{k}^{2}+ 900\,k+203,10000\,{k}^{3}+13500\,{k}^{2}+6085\,k+916,100000\,{k}^{4}+ 180000\,{k}^{3}+121650\,{k}^{2}+36590\,k+4133,1000000\,{k}^{5}+2250000 \,{k}^{4}+2027000\,{k}^{3}+914025\,{k}^{2}+206309\,k+18648],[4+10\,k,2+ 5\,k,2+3\,k,-2-6\,k,-3-7\,k,-1-2\,k]] {\it PISOT} \left( 10,100\,k+48 \right) =[[10,100\,k+48],[5+10\,k,-1-2 \,k]] {\it PISOT} \left( 10,100\,k+49 \right) =[[10,100\,k+49,1000\,{k}^{2}+ 980\,k+240],[4+10\,k,4+9\,k,2+4\,k]] {\it PISOT} \left( 10,100\,k+51 \right) =[[10,100\,k+51,1000\,{k}^{2}+ 1020\,k+260],[6+10\,k,-5-9\,k,2+4\,k]] {\it PISOT} \left( 10,100\,k+52 \right) =[[10,100\,k+52],[5+10\,k,1+2\, k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.972273950811336 {\it PISOT} \left( 10,100\,k+55 \right) =[[10,100\,k+55,1000\,{k}^{2}+ 1100\,k+303,10000\,{k}^{3}+16500\,{k}^{2}+9085\,k+1669,100000\,{k}^{4}+ 220000\,{k}^{3}+181650\,{k}^{2}+66710\,k+9193,1000000\,{k}^{5}+2750000 \,{k}^{4}+3027000\,{k}^{3}+1666975\,{k}^{2}+459259\,k+50636],[6+10\,k,- 3-5\,k,1+3\,k,4+6\,k,-4-7\,k,1+2\,k]] {\it PISOT} \left( 10,100\,k+57 \right) =[[10,100\,k+57],[5+10\,k,4+7\, k]] {\it PISOT} \left( 10,100\,k+59 \right) =[[10,100\,k+59,1000\,{k}^{2}+ 1180\,k+348],[7+10\,k,-7-11\,k,3+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.982594321008556 {\it PISOT} \left( 10,100\,k+61 \right) =[[10,100\,k+61,1000\,{k}^{2}+ 1220\,k+372,10000\,{k}^{3}+18300\,{k}^{2}+11161\,k+2269,100000\,{k}^{4} +244000\,{k}^{3}+223230\,{k}^{2}+90764\,k+13840,1000000\,{k}^{5}+ 3050000\,{k}^{4}+3720600\,{k}^{3}+2269201\,{k}^{2}+692002\,k+84419],[5+ 10\,k,6+11\,k,4+7\,k,2+3\,k,-k,-3-5\,k]] {\it PISOT} \left( 10,100\,k+62 \right) =[[10,100\,k+62],[7+10\,k,-5-8 \,k]] {\it PISOT} \left( 10,100\,k+65 \right) =[[10,100\,k+65,1000\,{k}^{2}+ 1300\,k+423],[6+10\,k,3+5\,k,2+3\,k]] {\it PISOT} \left( 10,100\,k+66 \right) =[[10,100\,k+66],[6+10\,k,4+6\, k]] {\it PISOT} \left( 10,100\,k+67 \right) =[[10,100\,k+67],[7+10\,k,-2-3 \,k]] {\it PISOT} \left( 10,100\,k+68 \right) =[[10,100\,k+68,1000\,{k}^{2}+ 1360\,k+462,10000\,{k}^{3}+20400\,{k}^{2}+13864\,k+3139,100000\,{k}^{4} +272000\,{k}^{3}+277320\,{k}^{2}+125612\,k+21328],[7+10\,k,-2-2\,k,4+6 \,k,1+k,-2-3\,k]] {\it PISOT} \left( 10,100\,k+71 \right) =[[10,100\,k+71,1000\,{k}^{2}+ 1420\,k+504],[7+10\,k,k,5+7\,k]] {\it PISOT} \left( 10,100\,k+74 \right) =[[10,100\,k+74],[7+10\,k,3+4\, k]] {\it PISOT} \left( 10,100\,k+75 \right) =[[10,100\,k+75,1000\,{k}^{2}+ 1500\,k+563],[7+10\,k,3+5\,k,6+8\,k]] {\it PISOT} \left( 10,100\,k+76 \right) =[[10,100\,k+76],[8+10\,k,-3-4 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.999999310740579 {\it PISOT} \left( 10,100\,k+81 \right) =[[10,100\,k+81,1000\,{k}^{2}+ 1620\,k+656,10000\,{k}^{3}+24300\,{k}^{2}+19681\,k+5313],[8+10\,k,k,6+8 \,k,4+5\,k]] {\it PISOT} \left( 10,100\,k+84 \right) =[[10,100\,k+84],[9+10\,k,-5-6 \,k]] {\it PISOT} \left( 10,100\,k+88 \right) =[[10,100\,k+88],[8+10\,k,7+8\, k]] {\it PISOT} \left( 10,100\,k+89 \right) =[[10,100\,k+89],[8+10\,k,8+9\, k]] {\it PISOT} \left( 10,100\,k+94 \right) =[[10,100\,k+94,1000\,{k}^{2}+ 1880\,k+884,10000\,{k}^{3}+28200\,{k}^{2}+26516\,k+8313,100000\,{k}^{4} +376000\,{k}^{3}+530280\,{k}^{2}+332452\,k+78174,1000000\,{k}^{5}+ 4700000\,{k}^{4}+8837600\,{k}^{3}+8310244\,{k}^{2}+3907780\,k+735135],[ 9+10\,k,4+4\,k,-2-2\,k,1+k,-1-k,1+k]] {\it PISOT} \left( 10,100\,k+95 \right) =[[10,100\,k+95,1000\,{k}^{2}+ 1900\,k+903,10000\,{k}^{3}+28500\,{k}^{2}+27085\,k+8583,100000\,{k}^{4} +380000\,{k}^{3}+541650\,{k}^{2}+343230\,k+81581],[9+10\,k,5+5\,k,-2-2 \,k,1+k,-1-k]] {\it PISOT} \left( 10,100\,k+96 \right) =[[10,100\,k+96,1000\,{k}^{2}+ 1920\,k+922,10000\,{k}^{3}+28800\,{k}^{2}+27656\,k+8855],[10+10\,k,-4-4 \,k,2+2\,k,-1-k]] {\it PISOT} \left( 10,100\,k+97 \right) =[[10,100\,k+97,1000\,{k}^{2}+ 1940\,k+941],[10+10\,k,-3-3\,k,1+k]] {\it PISOT} \left( 10,100\,k+98 \right) =[[10,100\,k+98],[10+10\,k,-2-2 \,k]] {\it PISOT} \left( 10,100\,k+99 \right) =[[10,100\,k+99],[10+10\,k,-1-k ]] {\it PISOT} \left( 11,121\,k+1 \right) =[[11,121\,k+1],[11\,k,k]] {\it PISOT} \left( 11,121\,k+2 \right) =[[11,121\,k+2],[11\,k,2\,k]] {\it PISOT} \left( 11,121\,k+3 \right) =[[11,121\,k+3,1331\,{k}^{2}+66 \,k+1],[11\,k,3\,k,k]] {\it PISOT} \left( 11,121\,k+4 \right) =[[11,121\,k+4,1331\,{k}^{2}+88 \,k+1],[11\,k,4\,k,k]] {\it PISOT} \left( 11,121\,k+5 \right) =[[11,121\,k+5,1331\,{k}^{2}+110 \,k+2,14641\,{k}^{3}+1815\,{k}^{2}+69\,k+1],[1+11\,k,-6\,k,-3\,k,-k]] {\it PISOT} \left( 11,121\,k+6 \right) =[[11,121\,k+6,1331\,{k}^{2}+132 \,k+3,14641\,{k}^{3}+2178\,{k}^{2}+102\,k+1],[11\,k,6\,k,3\,k,k]] {\it PISOT} \left( 11,121\,k+7 \right) =[[11,121\,k+7,1331\,{k}^{2}+154 \,k+4,14641\,{k}^{3}+2541\,{k}^{2}+137\,k+2,161051\,{k}^{4}+37268\,{k}^ {3}+3069\,{k}^{2}+100\,k+1],[11\,k,7\,k,4\,k,2\,k,k]] {\it PISOT} \left( 11,121\,k+12 \right) =[[11,121\,k+12],[2+11\,k,-1-10 \,k]] {\it PISOT} \left( 11,121\,k+13 \right) =[[11,121\,k+13],[2+11\,k,-1-9 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970518701889734 {\it PISOT} \left( 11,121\,k+15 \right) =[[11,121\,k+15,1331\,{k}^{2}+ 330\,k+20,14641\,{k}^{3}+5445\,{k}^{2}+665\,k+27],[1+11\,k,1+4\,k,-6\,k ,-1-8\,k]] {\it PISOT} \left( 11,121\,k+18 \right) =[[11,121\,k+18],[1+11\,k,1+7\, k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.973785918191569 {\it PISOT} \left( 11,121\,k+19 \right) =[[11,121\,k+19,1331\,{k}^{2}+ 418\,k+33,14641\,{k}^{3}+6897\,{k}^{2}+1087\,k+57,161051\,{k}^{4}+ 101156\,{k}^{3}+23892\,{k}^{2}+2508\,k+98,1771561\,{k}^{5}+1390895\,{k} ^{4}+437778\,{k}^{3}+68932\,{k}^{2}+5411\,k+168],[1+11\,k,1+8\,k,3\,k,1 +5\,k,-3\,k,-1-6\,k]] {\it PISOT} \left( 11,121\,k+20 \right) =[[11,121\,k+20,1331\,{k}^{2}+ 440\,k+36,14641\,{k}^{3}+7260\,{k}^{2}+1192\,k+65,161051\,{k}^{4}+ 106480\,{k}^{3}+26268\,{k}^{2}+2870\,k+117,1771561\,{k}^{5}+1464100\,{k }^{4}+482064\,{k}^{3}+79115\,{k}^{2}+6470\,k+211],[2+11\,k,-1-2\,k,1+7 \,k,2\,k,3\,k,1+6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.993536596228429 {\it PISOT} \left( 11,121\,k+23 \right) =[[11,121\,k+23,1331\,{k}^{2}+ 506\,k+48,14641\,{k}^{3}+8349\,{k}^{2}+1585\,k+100],[1+11\,k,2+12\,k,1+ 3\,k,-1-5\,k]] {\it PISOT} \left( 11,121\,k+24 \right) =[[11,121\,k+24,1331\,{k}^{2}+ 528\,k+52,14641\,{k}^{3}+8712\,{k}^{2}+1720\,k+113],[3+11\,k,-2-9\,k,2 \,k,1+5\,k]] {\it PISOT} \left( 11,121\,k+25 \right) =[[11,121\,k+25,1331\,{k}^{2}+ 550\,k+57,14641\,{k}^{3}+9075\,{k}^{2}+1879\,k+130],[2+11\,k,3\,k,1+7\, k,1+5\,k]] {\it PISOT} \left( 11,121\,k+29 \right) =[[11,121\,k+29],[3+11\,k,-1-4 \,k]] {\it PISOT} \left( 11,121\,k+30 \right) =[[11,121\,k+30],[2+11\,k,2+8\, k]] {\it PISOT} \left( 11,121\,k+36 \right) =[[11,121\,k+36,1331\,{k}^{2}+ 792\,k+118],[3+11\,k,3\,k,3+10\,k]] {\it PISOT} \left( 11,121\,k+39 \right) =[[11,121\,k+39,1331\,{k}^{2}+ 858\,k+138,14641\,{k}^{3}+14157\,{k}^{2}+4557\,k+488],[4+11\,k,-2-5\,k, 1+4\,k,1+3\,k]] {\it PISOT} \left( 11,121\,k+40 \right) =[[11,121\,k+40,1331\,{k}^{2}+ 880\,k+145],[3+11\,k,2+7\,k,1+3\,k]] {\it PISOT} \left( 11,121\,k+41 \right) =[[11,121\,k+41],[4+11\,k,-1-3 \,k]] {\it PISOT} \left( 11,121\,k+42 \right) =[[11,121\,k+42,1331\,{k}^{2}+ 924\,k+160,14641\,{k}^{3}+15246\,{k}^{2}+5284\,k+610,161051\,{k}^{4}+ 223608\,{k}^{3}+116292\,{k}^{2}+26860\,k+2326],[5+11\,k,-5-13\,k,2+5\,k ,-1-2\,k,1+3\,k]] {\it PISOT} \left( 11,121\,k+46 \right) =[[11,121\,k+46,1331\,{k}^{2}+ 1012\,k+192],[4+11\,k,2\,k,3+8\,k]] {\it PISOT} \left( 11,121\,k+48 \right) =[[11,121\,k+48,1331\,{k}^{2}+ 1056\,k+209],[4+11\,k,2+4\,k,-2-5\,k]] {\it PISOT} \left( 11,121\,k+49 \right) =[[11,121\,k+49],[4+11\,k,2+5\, k]] {\it PISOT} \left( 11,121\,k+50 \right) =[[11,121\,k+50,1331\,{k}^{2}+ 1100\,k+227,14641\,{k}^{3}+18150\,{k}^{2}+7494\,k+1031],[4+11\,k,3+6\,k ,-2-6\,k,-2-5\,k]] {\it PISOT} \left( 11,121\,k+51 \right) =[[11,121\,k+51,1331\,{k}^{2}+ 1122\,k+236],[6+11\,k,-7-15\,k,3+7\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.991049619414240 {\it PISOT} \left( 11,121\,k+53 \right) =[[11,121\,k+53,1331\,{k}^{2}+ 1166\,k+255,14641\,{k}^{3}+19239\,{k}^{2}+8419\,k+1227],[6+11\,k,-7-13 \,k,7+14\,k,-4-9\,k]] {\it PISOT} \left( 11,121\,k+57 \right) =[[11,121\,k+57,1331\,{k}^{2}+ 1254\,k+295,14641\,{k}^{3}+20691\,{k}^{2}+9739\,k+1527],[6+11\,k,-5-9\, k,4+8\,k,-1-2\,k]] {\it PISOT} \left( 11,121\,k+60 \right) =[[11,121\,k+60],[6+11\,k,-3-6 \,k]] {\it PISOT} \left( 11,121\,k+61 \right) =[[11,121\,k+61],[5+11\,k,3+6\, k]] {\it PISOT} \left( 11,121\,k+64 \right) =[[11,121\,k+64,1331\,{k}^{2}+ 1408\,k+372,14641\,{k}^{3}+23232\,{k}^{2}+12280\,k+2162],[5+11\,k,4+9\, k,4+8\,k,1+2\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.991046332718422 {\it PISOT} \left( 11,121\,k+68 \right) =[[11,121\,k+68,1331\,{k}^{2}+ 1496\,k+420,14641\,{k}^{3}+24684\,{k}^{2}+13864\,k+2594],[5+11\,k,6+13 \,k,7+14\,k,5+9\,k]] {\it PISOT} \left( 11,121\,k+70 \right) =[[11,121\,k+70,1331\,{k}^{2}+ 1540\,k+445],[5+11\,k,8+15\,k,4+7\,k]] {\it PISOT} \left( 11,121\,k+71 \right) =[[11,121\,k+71,1331\,{k}^{2}+ 1562\,k+458,14641\,{k}^{3}+25773\,{k}^{2}+15117\,k+2954],[7+11\,k,-3-6 \,k,-4-6\,k,3+5\,k]] {\it PISOT} \left( 11,121\,k+72 \right) =[[11,121\,k+72],[7+11\,k,-3-5 \,k]] {\it PISOT} \left( 11,121\,k+73 \right) =[[11,121\,k+73,1331\,{k}^{2}+ 1606\,k+484],[7+11\,k,-2-4\,k,-3-5\,k]] {\it PISOT} \left( 11,121\,k+75 \right) =[[11,121\,k+75,1331\,{k}^{2}+ 1650\,k+511],[7+11\,k,-2-2\,k,5+8\,k]] {\it PISOT} \left( 11,121\,k+79 \right) =[[11,121\,k+79,1331\,{k}^{2}+ 1738\,k+567,14641\,{k}^{3}+28677\,{k}^{2}+18715\,k+4069,161051\,{k}^{4} +420596\,{k}^{3}+411774\,{k}^{2}+179104\,k+29201],[6+11\,k,8+13\,k,3+5 \,k,1+2\,k,2+3\,k]] {\it PISOT} \left( 11,121\,k+80 \right) =[[11,121\,k+80],[7+11\,k,2+3\, k]] {\it PISOT} \left( 11,121\,k+81 \right) =[[11,121\,k+81,1331\,{k}^{2}+ 1782\,k+596],[8+11\,k,-5-7\,k,2+3\,k]] {\it PISOT} \left( 11,121\,k+82 \right) =[[11,121\,k+82,1331\,{k}^{2}+ 1804\,k+611,14641\,{k}^{3}+29766\,{k}^{2}+20166\,k+4553],[7+11\,k,3+5\, k,3+4\,k,-2-3\,k]] {\it PISOT} \left( 11,121\,k+85 \right) =[[11,121\,k+85,1331\,{k}^{2}+ 1870\,k+657],[8+11\,k,-3-3\,k,7+10\,k]] {\it PISOT} \left( 11,121\,k+91 \right) =[[11,121\,k+91],[9+11\,k,-6-8 \,k]] {\it PISOT} \left( 11,121\,k+92 \right) =[[11,121\,k+92],[8+11\,k,3+4\, k]] {\it PISOT} \left( 11,121\,k+96 \right) =[[11,121\,k+96,1331\,{k}^{2}+ 2112\,k+838,14641\,{k}^{3}+34848\,{k}^{2}+27652\,k+7315],[9+11\,k,-3-3 \,k,6+7\,k,-4-5\,k]] {\it PISOT} \left( 11,121\,k+97 \right) =[[11,121\,k+97,1331\,{k}^{2}+ 2134\,k+855,14641\,{k}^{3}+35211\,{k}^{2}+28219\,k+7536],[8+11\,k,7+9\, k,2+2\,k,-4-5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.993533177467672 {\it PISOT} \left( 11,121\,k+98 \right) =[[11,121\,k+98,1331\,{k}^{2}+ 2156\,k+873,14641\,{k}^{3}+35574\,{k}^{2}+28810\,k+7777],[10+11\,k,-10- 12\,k,2+3\,k,4+5\,k]] {\it PISOT} \left( 11,121\,k+101 \right) =[[11,121\,k+101,1331\,{k}^{2} +2222\,k+927,14641\,{k}^{3}+36663\,{k}^{2}+30595\,k+8508,161051\,{k}^{4 }+537724\,{k}^{3}+673134\,{k}^{2}+374430\,k+78086,1771561\,{k}^{5}+ 7393705\,{k}^{4}+12341274\,{k}^{3}+10298087\,{k}^{2}+4295837\,k+716669] ,[9+11\,k,1+2\,k,6+7\,k,-2-2\,k,3+3\,k,-5-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.973784811446376 {\it PISOT} \left( 11,121\,k+102 \right) =[[11,121\,k+102,1331\,{k}^{2} +2244\,k+946,14641\,{k}^{3}+37026\,{k}^{2}+31216\,k+8774,161051\,{k}^{4 }+543048\,{k}^{3}+686730\,{k}^{2}+386012\,k+81377,1771561\,{k}^{5}+ 7466910\,{k}^{4}+12589808\,{k}^{3}+10614642\,{k}^{2}+4475106\,k+754755] ,[10+11\,k,-7-8\,k,3+3\,k,-4-5\,k,-3-3\,k,5+6\,k]] {\it PISOT} \left( 11,121\,k+103 \right) =[[11,121\,k+103],[10+11\,k,-6 -7\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970516806497525 {\it PISOT} \left( 11,121\,k+106 \right) =[[11,121\,k+106,1331\,{k}^{2} +2332\,k+1021,14641\,{k}^{3}+38478\,{k}^{2}+33698\,k+9834],[10+11\,k,-3 -4\,k,-6-6\,k,7+8\,k]] {\it PISOT} \left( 11,121\,k+108 \right) =[[11,121\,k+108],[9+11\,k,8+9 \,k]] {\it PISOT} \left( 11,121\,k+109 \right) =[[11,121\,k+109],[9+11\,k,9+ 10\,k]] {\it PISOT} \left( 11,121\,k+114 \right) =[[11,121\,k+114,1331\,{k}^{2} +2508\,k+1181,14641\,{k}^{3}+41382\,{k}^{2}+38978\,k+12235,161051\,{k}^ {4}+606936\,{k}^{3}+857571\,{k}^{2}+538438\,k+126753],[11+11\,k,-7-7\,k ,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 11,121\,k+115 \right) =[[11,121\,k+115,1331\,{k}^{2} +2530\,k+1202,14641\,{k}^{3}+41745\,{k}^{2}+39669\,k+12564],[11+11\,k,- 6-6\,k,3+3\,k,-1-k]] {\it PISOT} \left( 11,121\,k+116 \right) =[[11,121\,k+116,1331\,{k}^{2} +2552\,k+1223,14641\,{k}^{3}+42108\,{k}^{2}+40362\,k+12894],[10+11\,k,6 +6\,k,-3-3\,k,1+k]] {\it PISOT} \left( 11,121\,k+117 \right) =[[11,121\,k+117,1331\,{k}^{2} +2574\,k+1244],[11+11\,k,-4-4\,k,1+k]] {\it PISOT} \left( 11,121\,k+118 \right) =[[11,121\,k+118,1331\,{k}^{2} +2596\,k+1266],[11+11\,k,-3-3\,k,1+k]] {\it PISOT} \left( 11,121\,k+119 \right) =[[11,121\,k+119],[11+11\,k,-2 -2\,k]] {\it PISOT} \left( 11,121\,k+120 \right) =[[11,121\,k+120],[11+11\,k,-1 -k]] {\it PISOT} \left( 12,144\,k+1 \right) =[[12,144\,k+1],[12\,k,k]] {\it PISOT} \left( 12,144\,k+2 \right) =[[12,144\,k+2],[12\,k,2\,k]] {\it PISOT} \left( 12,144\,k+3 \right) =[[12,144\,k+3,1728\,{k}^{2}+72 \,k+1],[12\,k,3\,k,k]] {\it PISOT} \left( 12,144\,k+4 \right) =[[12,144\,k+4,1728\,{k}^{2}+96 \,k+1],[12\,k,4\,k,k]] {\it PISOT} \left( 12,144\,k+5 \right) =[[12,144\,k+5,1728\,{k}^{2}+120 \,k+2,20736\,{k}^{3}+2160\,{k}^{2}+73\,k+1],[12\,k,5\,k,2\,k,k]] {\it PISOT} \left( 12,144\,k+6 \right) =[[12,144\,k+6,1728\,{k}^{2}+144 \,k+3,20736\,{k}^{3}+2592\,{k}^{2}+108\,k+2,248832\,{k}^{4}+41472\,{k}^ {3}+2592\,{k}^{2}+84\,k+1],[1+12\,k,-6\,k,-3\,k,-k,-k]] {\it PISOT} \left( 12,144\,k+7 \right) =[[12,144\,k+7,1728\,{k}^{2}+168 \,k+4,20736\,{k}^{3}+3024\,{k}^{2}+145\,k+2,248832\,{k}^{4}+48384\,{k}^ {3}+3492\,{k}^{2}+104\,k+1],[12\,k,7\,k,4\,k,2\,k,k]] {\it PISOT} \left( 12,144\,k+8 \right) =[[12,144\,k+8,1728\,{k}^{2}+192 \,k+5,20736\,{k}^{3}+3456\,{k}^{2}+184\,k+3,248832\,{k}^{4}+55296\,{k}^ {3}+4464\,{k}^{2}+152\,k+2,2985984\,{k}^{5}+829440\,{k}^{4}+89856\,{k}^ {3}+4688\,{k}^{2}+121\,k+1],[12\,k,8\,k,5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 12,144\,k+13 \right) =[[12,144\,k+13],[2+12\,k,-1-11 \,k]] {\it PISOT} \left( 12,144\,k+14 \right) =[[12,144\,k+14],[2+12\,k,-1-10 \,k]] {\it PISOT} \left( 12,144\,k+16 \right) =[[12,144\,k+16,1728\,{k}^{2}+ 384\,k+21],[12\,k,1+16\,k,1+9\,k]] {\it PISOT} \left( 12,144\,k+20 \right) =[[12,144\,k+20,1728\,{k}^{2}+ 480\,k+33],[2+12\,k,-4\,k,-1-7\,k]] {\it PISOT} \left( 12,144\,k+21 \right) =[[12,144\,k+21,1728\,{k}^{2}+ 504\,k+37],[2+12\,k,-1-3\,k,1+7\,k]] {\it PISOT} \left( 12,144\,k+23 \right) =[[12,144\,k+23,1728\,{k}^{2}+ 552\,k+44,20736\,{k}^{3}+9936\,{k}^{2}+1585\,k+84],[1+12\,k,2+11\,k,-3 \,k,-1-6\,k]] {\it PISOT} \left( 12,144\,k+28 \right) =[[12,144\,k+28,1728\,{k}^{2}+ 672\,k+65],[3+12\,k,-2-8\,k,1+5\,k]] {\it PISOT} \left( 12,144\,k+29 \right) =[[12,144\,k+29],[2+12\,k,1+5\, k]] {\it PISOT} \left( 12,144\,k+30 \right) =[[12,144\,k+30,1728\,{k}^{2}+ 720\,k+75,20736\,{k}^{3}+12960\,{k}^{2}+2700\,k+188],[3+12\,k,-1-6\,k,- 1-3\,k,1+5\,k]] {\it PISOT} \left( 12,144\,k+32 \right) =[[12,144\,k+32,1728\,{k}^{2}+ 768\,k+85],[2+12\,k,1+8\,k,2+9\,k]] {\it PISOT} \left( 12,144\,k+34 \right) =[[12,144\,k+34,1728\,{k}^{2}+ 816\,k+96,20736\,{k}^{3}+14688\,{k}^{2}+3460\,k+271,248832\,{k}^{4}+ 235008\,{k}^{3}+83088\,{k}^{2}+13032\,k+765],[3+12\,k,-1-2\,k,2+6\,k,-2 -7\,k,1+4\,k]] {\it PISOT} \left( 12,144\,k+37 \right) =[[12,144\,k+37,1728\,{k}^{2}+ 888\,k+114],[2+12\,k,3+13\,k,1+4\,k]] {\it PISOT} \left( 12,144\,k+38 \right) =[[12,144\,k+38,1728\,{k}^{2}+ 912\,k+120,20736\,{k}^{3}+16416\,{k}^{2}+4324\,k+379,248832\,{k}^{4}+ 262656\,{k}^{3}+103824\,{k}^{2}+18216\,k+1197],[3+12\,k,1+2\,k,-2-6\,k, 1+5\,k,1+4\,k]] {\it PISOT} \left( 12,144\,k+41 \right) =[[12,144\,k+41],[4+12\,k,-2-7 \,k]] {\it PISOT} \left( 12,144\,k+42 \right) =[[12,144\,k+42,1728\,{k}^{2}+ 1008\,k+147,20736\,{k}^{3}+18144\,{k}^{2}+5292\,k+515,248832\,{k}^{4}+ 290304\,{k}^{3}+127008\,{k}^{2}+24708\,k+1804],[3+12\,k,2+6\,k,-1-3\,k, 2\,k,2+7\,k]] {\it PISOT} \left( 12,144\,k+49 \right) =[[12,144\,k+49,1728\,{k}^{2}+ 1176\,k+200],[5+12\,k,-4-11\,k,1+3\,k]] {\it PISOT} \left( 12,144\,k+58 \right) =[[12,144\,k+58],[4+12\,k,4+10 \,k]] {\it PISOT} \left( 12,144\,k+59 \right) =[[12,144\,k+59,1728\,{k}^{2}+ 1416\,k+290,20736\,{k}^{3}+25488\,{k}^{2}+10441\,k+1425],[4+12\,k,4+11 \,k,2+6\,k,2+5\,k]] {\it PISOT} \left( 12,144\,k+61 \right) =[[12,144\,k+61,1728\,{k}^{2}+ 1464\,k+310],[5+12\,k,1+k,-3-7\,k]] {\it PISOT} \left( 12,144\,k+64 \right) =[[12,144\,k+64,1728\,{k}^{2}+ 1536\,k+341],[5+12\,k,1+4\,k,4+9\,k]] {\it PISOT} \left( 12,144\,k+68 \right) =[[12,144\,k+68,1728\,{k}^{2}+ 1632\,k+385,20736\,{k}^{3}+29376\,{k}^{2}+13864\,k+2180,248832\,{k}^{4} +470016\,{k}^{3}+332784\,{k}^{2}+104680\,k+12344],[6+12\,k,-2-4\,k,k,3+ 6\,k,-1-2\,k]] {\it PISOT} \left( 12,144\,k+70 \right) =[[12,144\,k+70],[6+12\,k,-1-2 \,k]] {\it PISOT} \left( 12,144\,k+71 \right) =[[12,144\,k+71,1728\,{k}^{2}+ 1704\,k+420],[6+12\,k,-1-k,3+6\,k]] {\it PISOT} \left( 12,144\,k+73 \right) =[[12,144\,k+73,1728\,{k}^{2}+ 1752\,k+444],[6+12\,k,k,3+6\,k]] {\it PISOT} \left( 12,144\,k+74 \right) =[[12,144\,k+74],[6+12\,k,1+2\, k]] {\it PISOT} \left( 12,144\,k+76 \right) =[[12,144\,k+76,1728\,{k}^{2}+ 1824\,k+481,20736\,{k}^{3}+32832\,{k}^{2}+17320\,k+3044,248832\,{k}^{4} +525312\,{k}^{3}+415728\,{k}^{2}+146168\,k+19264],[6+12\,k,2+4\,k,1+k,- 3-6\,k,-1-2\,k]] {\it PISOT} \left( 12,144\,k+80 \right) =[[12,144\,k+80,1728\,{k}^{2}+ 1920\,k+533],[7+12\,k,-3-4\,k,5+9\,k]] {\it PISOT} \left( 12,144\,k+83 \right) =[[12,144\,k+83,1728\,{k}^{2}+ 1992\,k+574],[7+12\,k,-k,-4-7\,k]] {\it PISOT} \left( 12,144\,k+85 \right) =[[12,144\,k+85,1728\,{k}^{2}+ 2040\,k+602,20736\,{k}^{3}+36720\,{k}^{2}+21673\,k+4264],[8+12\,k,-7-11 \,k,4+6\,k,-3-5\,k]] {\it PISOT} \left( 12,144\,k+86 \right) =[[12,144\,k+86],[8+12\,k,-6-10 \,k]] {\it PISOT} \left( 12,144\,k+90 \right) =[[12,144\,k+90,1728\,{k}^{2}+ 2160\,k+675,20736\,{k}^{3}+38880\,{k}^{2}+24300\,k+5063],[7+12\,k,3+6\, k,5+9\,k,5+8\,k]] {\it PISOT} \left( 12,144\,k+95 \right) =[[12,144\,k+95,1728\,{k}^{2}+ 2280\,k+752],[7+12\,k,7+11\,k,2+3\,k]] {\it PISOT} \left( 12,144\,k+102 \right) =[[12,144\,k+102,1728\,{k}^{2} +2448\,k+867,20736\,{k}^{3}+44064\,{k}^{2}+31212\,k+7370,248832\,{k}^{4 }+705024\,{k}^{3}+749088\,{k}^{2}+353748\,k+62649,2985984\,{k}^{5}+ 10575360\,{k}^{4}+14981760\,{k}^{3}+10612296\,{k}^{2}+3758745\,k+532551 ],[8+12\,k,4+6\,k,2+3\,k,1+2\,k,3+5\,k,5+7\,k]] {\it PISOT} \left( 12,144\,k+103 \right) =[[12,144\,k+103],[8+12\,k,5+7 \,k]] {\it PISOT} \left( 12,144\,k+106 \right) =[[12,144\,k+106,1728\,{k}^{2} +2544\,k+936,20736\,{k}^{3}+45792\,{k}^{2}+33700\,k+8265,248832\,{k}^{4 }+732672\,{k}^{3}+808848\,{k}^{2}+396792\,k+72981],[9+12\,k,-1-2\,k,-4- 6\,k,-4-5\,k,3+4\,k]] {\it PISOT} \left( 12,144\,k+107 \right) =[[12,144\,k+107,1728\,{k}^{2} +2568\,k+954],[10+12\,k,-10-13\,k,3+4\,k]] {\it PISOT} \left( 12,144\,k+110 \right) =[[12,144\,k+110,1728\,{k}^{2} +2640\,k+1008,20736\,{k}^{3}+47520\,{k}^{2}+36292\,k+9237,248832\,{k}^{ 4}+760320\,{k}^{3}+871056\,{k}^{2}+443448\,k+84645],[9+12\,k,1+2\,k,4+6 \,k,5+7\,k,3+4\,k]] {\it PISOT} \left( 12,144\,k+112 \right) =[[12,144\,k+112,1728\,{k}^{2} +2688\,k+1045],[10+12\,k,-7-8\,k,7+9\,k]] {\it PISOT} \left( 12,144\,k+114 \right) =[[12,144\,k+114,1728\,{k}^{2} +2736\,k+1083,20736\,{k}^{3}+49248\,{k}^{2}+38988\,k+10289,248832\,{k}^ {4}+787968\,{k}^{3}+935712\,{k}^{2}+493860\,k+97750],[10+12\,k,-5-6\,k, 3+3\,k,-6-7\,k,4+5\,k]] {\it PISOT} \left( 12,144\,k+115 \right) =[[12,144\,k+115],[10+12\,k,-4 -5\,k]] {\it PISOT} \left( 12,144\,k+116 \right) =[[12,144\,k+116,1728\,{k}^{2} +2784\,k+1121],[9+12\,k,6+8\,k,4+5\,k]] {\it PISOT} \left( 12,144\,k+121 \right) =[[12,144\,k+121,1728\,{k}^{2} +2904\,k+1220,20736\,{k}^{3}+52272\,{k}^{2}+43921\,k+12301],[11+12\,k,- 9-11\,k,-3-3\,k,5+6\,k]] {\it PISOT} \left( 12,144\,k+123 \right) =[[12,144\,k+123,1728\,{k}^{2} +2952\,k+1261],[10+12\,k,2+3\,k,6+7\,k]] {\it PISOT} \left( 12,144\,k+124 \right) =[[12,144\,k+124,1728\,{k}^{2} +2976\,k+1281],[10+12\,k,4+4\,k,-6-7\,k]] {\it PISOT} \left( 12,144\,k+126 \right) =[[12,144\,k+126,1728\,{k}^{2} +3024\,k+1323,20736\,{k}^{3}+54432\,{k}^{2}+47628\,k+13892],[10+12\,k,5 +6\,k,2+3\,k,7+8\,k]] {\it PISOT} \left( 12,144\,k+128 \right) =[[12,144\,k+128,1728\,{k}^{2} +3072\,k+1365],[12+12\,k,-15-16\,k,8+9\,k]] {\it PISOT} \left( 12,144\,k+130 \right) =[[12,144\,k+130],[10+12\,k,9+ 10\,k]] {\it PISOT} \left( 12,144\,k+131 \right) =[[12,144\,k+131],[10+12\,k,10 +11\,k]] {\it PISOT} \left( 12,144\,k+136 \right) =[[12,144\,k+136,1728\,{k}^{2} +3264\,k+1541,20736\,{k}^{3}+58752\,{k}^{2}+55480\,k+17461,248832\,{k}^ {4}+940032\,{k}^{3}+1331568\,{k}^{2}+838216\,k+197850,2985984\,{k}^{5}+ 14100480\,{k}^{4}+26631936\,{k}^{3}+25148080\,{k}^{2}+11872473\,k+ 2241832],[12+12\,k,-8-8\,k,5+5\,k,-3-3\,k,2+2\,k,-1-k]] {\it PISOT} \left( 12,144\,k+137 \right) =[[12,144\,k+137,1728\,{k}^{2} +3288\,k+1564,20736\,{k}^{3}+59184\,{k}^{2}+56305\,k+17855,248832\,{k}^ {4}+946944\,{k}^{3}+1351332\,{k}^{2}+857056\,k+203837],[12+12\,k,-7-7\, k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 12,144\,k+138 \right) =[[12,144\,k+138,1728\,{k}^{2} +3312\,k+1587,20736\,{k}^{3}+59616\,{k}^{2}+57132\,k+18251],[12+12\,k,- 6-6\,k,3+3\,k,-1-k]] {\it PISOT} \left( 12,144\,k+139 \right) =[[12,144\,k+139,1728\,{k}^{2} +3336\,k+1610,20736\,{k}^{3}+60048\,{k}^{2}+57961\,k+18648],[12+12\,k,- 5-5\,k,2+2\,k,-1-k]] {\it PISOT} \left( 12,144\,k+140 \right) =[[12,144\,k+140,1728\,{k}^{2} +3360\,k+1633],[12+12\,k,-4-4\,k,1+k]] {\it PISOT} \left( 12,144\,k+141 \right) =[[12,144\,k+141,1728\,{k}^{2} +3384\,k+1657],[12+12\,k,-3-3\,k,1+k]] {\it PISOT} \left( 12,144\,k+142 \right) =[[12,144\,k+142],[12+12\,k,-2 -2\,k]] {\it PISOT} \left( 12,144\,k+143 \right) =[[12,144\,k+143],[12+12\,k,-1 -k]] {\it PISOT} \left( 13,169\,k+1 \right) =[[13,169\,k+1],[13\,k,k]] {\it PISOT} \left( 13,169\,k+2 \right) =[[13,169\,k+2],[13\,k,2\,k]] {\it PISOT} \left( 13,169\,k+3 \right) =[[13,169\,k+3,2197\,{k}^{2}+78 \,k+1],[13\,k,3\,k,k]] {\it PISOT} \left( 13,169\,k+4 \right) =[[13,169\,k+4,2197\,{k}^{2}+104 \,k+1],[13\,k,4\,k,k]] {\it PISOT} \left( 13,169\,k+5 \right) =[[13,169\,k+5,2197\,{k}^{2}+130 \,k+2,28561\,{k}^{3}+2535\,{k}^{2}+77\,k+1],[13\,k,5\,k,2\,k,k]] {\it PISOT} \left( 13,169\,k+6 \right) =[[13,169\,k+6,2197\,{k}^{2}+156 \,k+3,28561\,{k}^{3}+3042\,{k}^{2}+114\,k+1],[13\,k,6\,k,3\,k,k]] {\it PISOT} \left( 13,169\,k+7 \right) =[[13,169\,k+7,2197\,{k}^{2}+182 \,k+4,28561\,{k}^{3}+3549\,{k}^{2}+153\,k+2,371293\,{k}^{4}+61516\,{k}^ {3}+3939\,{k}^{2}+108\,k+1],[13\,k,7\,k,4\,k,2\,k,k]] {\it PISOT} \left( 13,169\,k+8 \right) =[[13,169\,k+8,2197\,{k}^{2}+208 \,k+5,28561\,{k}^{3}+4056\,{k}^{2}+194\,k+3,371293\,{k}^{4}+70304\,{k}^ {3}+5031\,{k}^{2}+158\,k+2,4826809\,{k}^{5}+1142440\,{k}^{4}+108836\,{k }^{3}+5153\,{k}^{2}+125\,k+1],[13\,k,8\,k,5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 13,169\,k+14 \right) =[[13,169\,k+14],[2+13\,k,-1-12 \,k]] {\it PISOT} \left( 13,169\,k+15 \right) =[[13,169\,k+15],[2+13\,k,-1-11 \,k]] {\it PISOT} \left( 13,169\,k+19 \right) =[[13,169\,k+19,2197\,{k}^{2}+ 494\,k+28],[1+13\,k,6\,k,1+9\,k]] {\it PISOT} \left( 13,169\,k+21 \right) =[[13,169\,k+21],[1+13\,k,1+8\, k]] {\it PISOT} \left( 13,169\,k+22 \right) =[[13,169\,k+22,2197\,{k}^{2}+ 572\,k+37,28561\,{k}^{3}+11154\,{k}^{2}+1446\,k+62,371293\,{k}^{4}+ 193336\,{k}^{3}+37635\,{k}^{2}+3240\,k+104],[2+13\,k,-1-4\,k,1+6\,k,-1- 3\,k,1+8\,k]] {\it PISOT} \left( 13,169\,k+23 \right) =[[13,169\,k+23,2197\,{k}^{2}+ 598\,k+41,28561\,{k}^{3}+11661\,{k}^{2}+1595\,k+73,371293\,{k}^{4}+ 202124\,{k}^{3}+41418\,{k}^{2}+3784\,k+130],[2+13\,k,-3\,k,-1-5\,k,4\,k ,1+7\,k]] {\it PISOT} \left( 13,169\,k+24 \right) =[[13,169\,k+24,2197\,{k}^{2}+ 624\,k+44],[1+13\,k,1+11\,k,1+7\,k]] {\it PISOT} \left( 13,169\,k+28 \right) =[[13,169\,k+28,2197\,{k}^{2}+ 728\,k+60],[1+13\,k,2+15\,k,1+6\,k]] {\it PISOT} \left( 13,169\,k+29 \right) =[[13,169\,k+29,2197\,{k}^{2}+ 754\,k+65],[2+13\,k,1+3\,k,-1-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.985649982540292 {\it PISOT} \left( 13,169\,k+32 \right) =[[13,169\,k+32,2197\,{k}^{2}+ 832\,k+79,28561\,{k}^{3}+16224\,{k}^{2}+3078\,k+195,371293\,{k}^{4}+ 281216\,{k}^{3}+79989\,{k}^{2}+10126\,k+481,4826809\,{k}^{5}+4569760\,{ k}^{4}+1732588\,{k}^{3}+328817\,{k}^{2}+31227\,k+1186],[2+13\,k,1+6\,k, 1+2\,k,-1-8\,k,-1-7\,k,-1-5\,k]] {\it PISOT} \left( 13,169\,k+33 \right) =[[13,169\,k+33,2197\,{k}^{2}+ 858\,k+84],[2+13\,k,1+7\,k,1+5\,k]] {\it PISOT} \left( 13,169\,k+34 \right) =[[13,169\,k+34],[3+13\,k,-1-5 \,k]] {\it PISOT} \left( 13,169\,k+35 \right) =[[13,169\,k+35,2197\,{k}^{2}+ 910\,k+94,28561\,{k}^{3}+17745\,{k}^{2}+3669\,k+252,371293\,{k}^{4}+ 307580\,{k}^{3}+95433\,{k}^{2}+13132\,k+676],[3+13\,k,-1-4\,k,1+2\,k,-2 -8\,k,1+5\,k]] {\it PISOT} \left( 13,169\,k+37 \right) =[[13,169\,k+37,2197\,{k}^{2}+ 962\,k+105],[4+13\,k,-4-15\,k,2+9\,k]] {\it PISOT} \left( 13,169\,k+38 \right) =[[13,169\,k+38,2197\,{k}^{2}+ 988\,k+111],[2+13\,k,2+12\,k,2+9\,k]] {\it PISOT} \left( 13,169\,k+41 \right) =[[13,169\,k+41,2197\,{k}^{2}+ 1066\,k+129],[4+13\,k,-3-11\,k,1+4\,k]] {\it PISOT} \left( 13,169\,k+43 \right) =[[13,169\,k+43],[3+13\,k,1+4\, k]] {\it PISOT} \left( 13,169\,k+44 \right) =[[13,169\,k+44,2197\,{k}^{2}+ 1144\,k+149,28561\,{k}^{3}+22308\,{k}^{2}+5810\,k+505],[3+13\,k,2+5\,k, -2-9\,k,-1-4\,k]] {\it PISOT} \left( 13,169\,k+46 \right) =[[13,169\,k+46,2197\,{k}^{2}+ 1196\,k+163],[5+13\,k,-6-19\,k,3+11\,k]] {\it PISOT} \left( 13,169\,k+48 \right) =[[13,169\,k+48,2197\,{k}^{2}+ 1248\,k+177],[3+13\,k,2+9\,k,2+7\,k]] {\it PISOT} \left( 13,169\,k+51 \right) =[[13,169\,k+51,2197\,{k}^{2}+ 1326\,k+200],[5+13\,k,-5-14\,k,3+10\,k]] {\it PISOT} \left( 13,169\,k+55 \right) =[[13,169\,k+55],[4+13\,k,1+3\, k]] {\it PISOT} \left( 13,169\,k+56 \right) =[[13,169\,k+56],[5+13\,k,-3-9 \,k]] {\it PISOT} \left( 13,169\,k+57 \right) =[[13,169\,k+57,2197\,{k}^{2}+ 1482\,k+250],[4+13\,k,1+5\,k,3+9\,k]] {\it PISOT} \left( 13,169\,k+58 \right) =[[13,169\,k+58,2197\,{k}^{2}+ 1508\,k+259,28561\,{k}^{3}+29406\,{k}^{2}+10098\,k+1157],[5+13\,k,-3-7 \,k,3+8\,k,-1-3\,k]] {\it PISOT} \left( 13,169\,k+59 \right) =[[13,169\,k+59,2197\,{k}^{2}+ 1534\,k+268,28561\,{k}^{3}+29913\,{k}^{2}+10449\,k+1217,371293\,{k}^{4} +518492\,{k}^{3}+271635\,{k}^{2}+63266\,k+5526],[5+13\,k,-2-6\,k,-1-k,3 +8\,k,-1-3\,k]] {\it PISOT} \left( 13,169\,k+61 \right) =[[13,169\,k+61,2197\,{k}^{2}+ 1586\,k+286],[6+13\,k,-7-17\,k,4+11\,k]] {\it PISOT} \left( 13,169\,k+64 \right) =[[13,169\,k+64,2197\,{k}^{2}+ 1664\,k+315],[5+13\,k,-1-k,3+8\,k]] {\it PISOT} \left( 13,169\,k+66 \right) =[[13,169\,k+66,2197\,{k}^{2}+ 1716\,k+335,28561\,{k}^{3}+33462\,{k}^{2}+13066\,k+1700,371293\,{k}^{4} +580008\,{k}^{3}+339729\,{k}^{2}+88420\,k+8627],[5+13\,k,k,2+5\,k,-k,-2 -5\,k]] {\it PISOT} \left( 13,169\,k+68 \right) =[[13,169\,k+68],[6+13\,k,-4-10 \,k]] {\it PISOT} \left( 13,169\,k+69 \right) =[[13,169\,k+69,2197\,{k}^{2}+ 1794\,k+366,28561\,{k}^{3}+34983\,{k}^{2}+14277\,k+1941],[6+13\,k,-4-9 \,k,2+4\,k,-2-5\,k]] {\it PISOT} \left( 13,169\,k+71 \right) =[[13,169\,k+71,2197\,{k}^{2}+ 1846\,k+388,28561\,{k}^{3}+35997\,{k}^{2}+15129\,k+2120,371293\,{k}^{4} +623948\,{k}^{3}+393315\,{k}^{2}+110216\,k+11584],[5+13\,k,3+6\,k,-3-6 \,k,2+6\,k,3+7\,k]] {\it PISOT} \left( 13,169\,k+72 \right) =[[13,169\,k+72],[5+13\,k,3+7\, k]] {\it PISOT} \left( 13,169\,k+75 \right) =[[13,169\,k+75,2197\,{k}^{2}+ 1950\,k+433],[6+13\,k,-2-3\,k,4+9\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.997296608670196 {\it PISOT} \left( 13,169\,k+82 \right) =[[13,169\,k+82,2197\,{k}^{2}+ 2132\,k+517,28561\,{k}^{3}+41574\,{k}^{2}+20166\,k+3260],[6+13\,k,1+4\, k,6+12\,k,-1-2\,k]] {\it PISOT} \left( 13,169\,k+83 \right) =[[13,169\,k+83,2197\,{k}^{2}+ 2158\,k+530,28561\,{k}^{3}+42081\,{k}^{2}+20669\,k+3384],[7+13\,k,-4-8 \,k,k,3+6\,k]] {\it PISOT} \left( 13,169\,k+84 \right) =[[13,169\,k+84],[6+13\,k,3+6\, k]] {\it PISOT} \left( 13,169\,k+85 \right) =[[13,169\,k+85],[7+13\,k,-3-6 \,k]] {\it PISOT} \left( 13,169\,k+86 \right) =[[13,169\,k+86,2197\,{k}^{2}+ 2236\,k+569,28561\,{k}^{3}+43602\,{k}^{2}+22190\,k+3765],[6+13\,k,4+8\, k,1+k,-3-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.997293845746745 {\it PISOT} \left( 13,169\,k+87 \right) =[[13,169\,k+87,2197\,{k}^{2}+ 2262\,k+582,28561\,{k}^{3}+44109\,{k}^{2}+22701\,k+3893],[7+13\,k,-3-4 \,k,6+12\,k,1+2\,k]] {\it PISOT} \left( 13,169\,k+94 \right) =[[13,169\,k+94,2197\,{k}^{2}+ 2444\,k+680],[7+13\,k,1+3\,k,5+9\,k]] {\it PISOT} \left( 13,169\,k+97 \right) =[[13,169\,k+97],[8+13\,k,-4-7 \,k]] {\it PISOT} \left( 13,169\,k+98 \right) =[[13,169\,k+98,2197\,{k}^{2}+ 2548\,k+739,28561\,{k}^{3}+49686\,{k}^{2}+28818\,k+5573,371293\,{k}^{4} +861224\,{k}^{3}+749229\,{k}^{2}+289742\,k+42028],[8+13\,k,-3-6\,k,-3-6 \,k,-4-6\,k,4+7\,k]] {\it PISOT} \left( 13,169\,k+100 \right) =[[13,169\,k+100,2197\,{k}^{2} +2600\,k+769,28561\,{k}^{3}+50700\,{k}^{2}+29994\,k+5914],[7+13\,k,5+9 \,k,2+4\,k,3+5\,k]] {\it PISOT} \left( 13,169\,k+101 \right) =[[13,169\,k+101],[7+13\,k,6+ 10\,k]] {\it PISOT} \left( 13,169\,k+103 \right) =[[13,169\,k+103,2197\,{k}^{2} +2678\,k+816,28561\,{k}^{3}+52221\,{k}^{2}+31825\,k+6465,371293\,{k}^{4 }+905164\,{k}^{3}+827463\,{k}^{2}+336186\,k+51221],[8+13\,k,-1-k,3+5\,k ,1+k,-3-5\,k]] {\it PISOT} \left( 13,169\,k+105 \right) =[[13,169\,k+105,2197\,{k}^{2} +2730\,k+848],[8+13\,k,k,5+8\,k]] {\it PISOT} \left( 13,169\,k+108 \right) =[[13,169\,k+108,2197\,{k}^{2} +2808\,k+897],[7+13\,k,10+17\,k,7+11\,k]] {\it PISOT} \left( 13,169\,k+110 \right) =[[13,169\,k+110,2197\,{k}^{2} +2860\,k+931,28561\,{k}^{3}+55770\,{k}^{2}+36306\,k+7880,371293\,{k}^{4 }+966680\,{k}^{3}+943917\,{k}^{2}+409700\,k+66696],[8+13\,k,4+6\,k,-k,- 5-8\,k,-2-3\,k]] {\it PISOT} \left( 13,169\,k+111 \right) =[[13,169\,k+111,2197\,{k}^{2} +2886\,k+948,28561\,{k}^{3}+56277\,{k}^{2}+36969\,k+8096],[8+13\,k,4+7 \,k,5+8\,k,2+3\,k]] {\it PISOT} \left( 13,169\,k+112 \right) =[[13,169\,k+112,2197\,{k}^{2} +2912\,k+965],[9+13\,k,-4-5\,k,6+9\,k]] {\it PISOT} \left( 13,169\,k+113 \right) =[[13,169\,k+113],[8+13\,k,6+9 \,k]] {\it PISOT} \left( 13,169\,k+114 \right) =[[13,169\,k+114],[9+13\,k,-2- 3\,k]] {\it PISOT} \left( 13,169\,k+118 \right) =[[13,169\,k+118,2197\,{k}^{2} +3068\,k+1071],[8+13\,k,9+14\,k,7+10\,k]] {\it PISOT} \left( 13,169\,k+121 \right) =[[13,169\,k+121,2197\,{k}^{2} +3146\,k+1126],[10+13\,k,-7-9\,k,5+7\,k]] {\it PISOT} \left( 13,169\,k+123 \right) =[[13,169\,k+123,2197\,{k}^{2} +3198\,k+1164],[8+13\,k,13+19\,k,8+11\,k]] {\it PISOT} \left( 13,169\,k+125 \right) =[[13,169\,k+125,2197\,{k}^{2} +3250\,k+1202,28561\,{k}^{3}+63375\,{k}^{2}+46877\,k+11558],[10+13\,k,- 3-5\,k,-7-9\,k,3+4\,k]] {\it PISOT} \left( 13,169\,k+126 \right) =[[13,169\,k+126],[10+13\,k,-3 -4\,k]] {\it PISOT} \left( 13,169\,k+128 \right) =[[13,169\,k+128,2197\,{k}^{2} +3328\,k+1260],[9+13\,k,8+11\,k,3+4\,k]] {\it PISOT} \left( 13,169\,k+131 \right) =[[13,169\,k+131,2197\,{k}^{2} +3406\,k+1320],[11+13\,k,-10-12\,k,7+9\,k]] {\it PISOT} \left( 13,169\,k+132 \right) =[[13,169\,k+132,2197\,{k}^{2} +3432\,k+1340],[9+13\,k,11+15\,k,7+9\,k]] {\it PISOT} \left( 13,169\,k+134 \right) =[[13,169\,k+134,2197\,{k}^{2} +3484\,k+1381,28561\,{k}^{3}+67938\,{k}^{2}+53862\,k+14233,371293\,{k}^ {4}+1177592\,{k}^{3}+1400451\,{k}^{2}+740166\,k+146690],[10+13\,k,3+4\, k,1+2\,k,6+8\,k,4+5\,k]] {\it PISOT} \left( 13,169\,k+135 \right) =[[13,169\,k+135],[10+13\,k,4+ 5\,k]] {\it PISOT} \left( 13,169\,k+136 \right) =[[13,169\,k+136,2197\,{k}^{2} +3536\,k+1423],[11+13\,k,-6-7\,k,4+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.985646655704477 {\it PISOT} \left( 13,169\,k+137 \right) =[[13,169\,k+137,2197\,{k}^{2} +3562\,k+1444,28561\,{k}^{3}+69459\,{k}^{2}+56313\,k+15220,371293\,{k}^ {4}+1203956\,{k}^{3}+1464099\,{k}^{2}+791376\,k+160421,4826809\,{k}^{5} +19564285\,{k}^{4}+31721638\,{k}^{3}+25718477\,{k}^{2}+10426362\,k+ 1690861],[11+13\,k,-5-6\,k,1+2\,k,7+8\,k,-6-7\,k,4+5\,k]] {\it PISOT} \left( 13,169\,k+140 \right) =[[13,169\,k+140,2197\,{k}^{2} +3640\,k+1508],[11+13\,k,-2-3\,k,-5-6\,k]] {\it PISOT} \left( 13,169\,k+141 \right) =[[13,169\,k+141,2197\,{k}^{2} +3666\,k+1529],[12+13\,k,-13-15\,k,5+6\,k]] {\it PISOT} \left( 13,169\,k+145 \right) =[[13,169\,k+145,2197\,{k}^{2} +3770\,k+1617],[12+13\,k,-10-11\,k,6+7\,k]] {\it PISOT} \left( 13,169\,k+146 \right) =[[13,169\,k+146,2197\,{k}^{2} +3796\,k+1640,28561\,{k}^{3}+74022\,{k}^{2}+63956\,k+18422,371293\,{k}^ {4}+1283048\,{k}^{3}+1662804\,{k}^{2}+957852\,k+206933],[11+13\,k,3+3\, k,-4-5\,k,-4-4\,k,6+7\,k]] {\it PISOT} \left( 13,169\,k+147 \right) =[[13,169\,k+147,2197\,{k}^{2} +3822\,k+1662,28561\,{k}^{3}+74529\,{k}^{2}+64821\,k+18791,371293\,{k}^ {4}+1291836\,{k}^{3}+1685385\,{k}^{2}+977194\,k+212456],[11+13\,k,3+4\, k,5+6\,k,2+3\,k,7+8\,k]] {\it PISOT} \left( 13,169\,k+148 \right) =[[13,169\,k+148],[12+13\,k,-7 -8\,k]] {\it PISOT} \left( 13,169\,k+150 \right) =[[13,169\,k+150,2197\,{k}^{2} +3900\,k+1731],[12+13\,k,-6-6\,k,8+9\,k]] {\it PISOT} \left( 13,169\,k+154 \right) =[[13,169\,k+154],[11+13\,k,10 +11\,k]] {\it PISOT} \left( 13,169\,k+155 \right) =[[13,169\,k+155],[11+13\,k,11 +12\,k]] {\it PISOT} \left( 13,169\,k+161 \right) =[[13,169\,k+161,2197\,{k}^{2} +4186\,k+1994,28561\,{k}^{3}+81627\,{k}^{2}+77765\,k+24696,371293\,{k}^ {4}+1414868\,{k}^{3}+2021877\,{k}^{2}+1284164\,k+305864,4826809\,{k}^{5 }+22991605\,{k}^{4}+43807166\,{k}^{3}+41734805\,{k}^{2}+19880612\,k+ 3788176],[13+13\,k,-8-8\,k,5+5\,k,-3-3\,k,2+2\,k,-1-k]] {\it PISOT} \left( 13,169\,k+162 \right) =[[13,169\,k+162,2197\,{k}^{2} +4212\,k+2019,28561\,{k}^{3}+82134\,{k}^{2}+78738\,k+25163,371293\,{k}^ {4}+1423656\,{k}^{3}+2047149\,{k}^{2}+1308394\,k+313609],[13+13\,k,-7-7 \,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 13,169\,k+163 \right) =[[13,169\,k+163,2197\,{k}^{2} +4238\,k+2044,28561\,{k}^{3}+82641\,{k}^{2}+79713\,k+25632],[13+13\,k,- 6-6\,k,3+3\,k,-1-k]] {\it PISOT} \left( 13,169\,k+164 \right) =[[13,169\,k+164,2197\,{k}^{2} +4264\,k+2069,28561\,{k}^{3}+83148\,{k}^{2}+80690\,k+26102],[13+13\,k,- 5-5\,k,2+2\,k,-1-k]] {\it PISOT} \left( 13,169\,k+165 \right) =[[13,169\,k+165,2197\,{k}^{2} +4290\,k+2094],[13+13\,k,-4-4\,k,1+k]] {\it PISOT} \left( 13,169\,k+166 \right) =[[13,169\,k+166,2197\,{k}^{2} +4316\,k+2120],[13+13\,k,-3-3\,k,1+k]] {\it PISOT} \left( 13,169\,k+167 \right) =[[13,169\,k+167],[13+13\,k,-2 -2\,k]] {\it PISOT} \left( 13,169\,k+168 \right) =[[13,169\,k+168],[13+13\,k,-1 -k]] {\it PISOT} \left( 14,196\,k+1 \right) =[[14,196\,k+1],[14\,k,k]] {\it PISOT} \left( 14,196\,k+2 \right) =[[14,196\,k+2],[14\,k,2\,k]] {\it PISOT} \left( 14,196\,k+3 \right) =[[14,196\,k+3,2744\,{k}^{2}+84 \,k+1],[14\,k,3\,k,k]] {\it PISOT} \left( 14,196\,k+4 \right) =[[14,196\,k+4,2744\,{k}^{2}+112 \,k+1],[14\,k,4\,k,k]] {\it PISOT} \left( 14,196\,k+5 \right) =[[14,196\,k+5,2744\,{k}^{2}+140 \,k+2,38416\,{k}^{3}+2940\,{k}^{2}+81\,k+1],[14\,k,5\,k,2\,k,k]] {\it PISOT} \left( 14,196\,k+6 \right) =[[14,196\,k+6,2744\,{k}^{2}+168 \,k+3,38416\,{k}^{3}+3528\,{k}^{2}+120\,k+1],[14\,k,6\,k,3\,k,k]] {\it PISOT} \left( 14,196\,k+7 \right) =[[14,196\,k+7,2744\,{k}^{2}+196 \,k+4,38416\,{k}^{3}+4116\,{k}^{2}+161\,k+2,537824\,{k}^{4}+76832\,{k}^ {3}+4410\,{k}^{2}+112\,k+1],[14\,k,7\,k,4\,k,2\,k,k]] {\it PISOT} \left( 14,196\,k+8 \right) =[[14,196\,k+8,2744\,{k}^{2}+224 \,k+5,38416\,{k}^{3}+4704\,{k}^{2}+204\,k+3,537824\,{k}^{4}+87808\,{k}^ {3}+5628\,{k}^{2}+164\,k+2,7529536\,{k}^{5}+1536640\,{k}^{4}+130144\,{k }^{3}+5636\,{k}^{2}+129\,k+1],[1+14\,k,-6\,k,-3\,k,-2\,k,-k,-k]] {\it PISOT} \left( 14,196\,k+15 \right) =[[14,196\,k+15],[2+14\,k,-1-13 \,k]] {\it PISOT} \left( 14,196\,k+16 \right) =[[14,196\,k+16],[2+14\,k,-1-12 \,k]] {\it PISOT} \left( 14,196\,k+19 \right) =[[14,196\,k+19,2744\,{k}^{2}+ 532\,k+26,38416\,{k}^{3}+11172\,{k}^{2}+1089\,k+36],[1+14\,k,5\,k,7\,k, 1+10\,k]] {\it PISOT} \left( 14,196\,k+29 \right) =[[14,196\,k+29,2744\,{k}^{2}+ 812\,k+60,38416\,{k}^{3}+17052\,{k}^{2}+2521\,k+124],[1+14\,k,1+15\,k,2 +17\,k,1+7\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.991479277104490 {\it PISOT} \left( 14,196\,k+31 \right) =[[14,196\,k+31,2744\,{k}^{2}+ 868\,k+69,38416\,{k}^{3}+18228\,{k}^{2}+2893\,k+154,537824\,{k}^{4}+ 340256\,{k}^{3}+80934\,{k}^{2}+8590\,k+344,7529536\,{k}^{5}+5954480\,{k }^{4}+1887480\,{k}^{3}+300019\,{k}^{2}+23941\,k+768],[3+14\,k,-2-11\,k, 1+4\,k,-1-5\,k,3\,k,1+6\,k]] {\it PISOT} \left( 14,196\,k+33 \right) =[[14,196\,k+33,2744\,{k}^{2}+ 924\,k+78],[2+14\,k,5\,k,2+12\,k]] {\it PISOT} \left( 14,196\,k+35 \right) =[[14,196\,k+35,2744\,{k}^{2}+ 980\,k+88],[1+14\,k,3+21\,k,2+11\,k]] {\it PISOT} \left( 14,196\,k+38 \right) =[[14,196\,k+38,2744\,{k}^{2}+ 1064\,k+103,38416\,{k}^{3}+22344\,{k}^{2}+4328\,k+279,537824\,{k}^{4}+ 417088\,{k}^{3}+121212\,{k}^{2}+15640\,k+756],[2+14\,k,1+10\,k,2+13\,k, 1+7\,k,1+5\,k]] {\it PISOT} \left( 14,196\,k+39 \right) =[[14,196\,k+39,2744\,{k}^{2}+ 1092\,k+109,38416\,{k}^{3}+22932\,{k}^{2}+4573\,k+305],[2+14\,k,2+11\,k ,1+3\,k,-1-5\,k]] {\it PISOT} \left( 14,196\,k+40 \right) =[[14,196\,k+40,2744\,{k}^{2}+ 1120\,k+114,38416\,{k}^{3}+23520\,{k}^{2}+4792\,k+325],[3+14\,k,-1-2\,k ,2+8\,k,-1-5\,k]] {\it PISOT} \left( 14,196\,k+43 \right) =[[14,196\,k+43,2744\,{k}^{2}+ 1204\,k+132,38416\,{k}^{3}+25284\,{k}^{2}+5545\,k+405],[3+14\,k,k,3\,k, 2+9\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.982980847864889 {\it PISOT} \left( 14,196\,k+44 \right) =[[14,196\,k+44,2744\,{k}^{2}+ 1232\,k+138,38416\,{k}^{3}+25872\,{k}^{2}+5800\,k+433],[3+14\,k,2\,k,2+ 6\,k,-2-9\,k]] {\it PISOT} \left( 14,196\,k+45 \right) =[[14,196\,k+45,2744\,{k}^{2}+ 1260\,k+145],[2+14\,k,3+17\,k,3+13\,k]] {\it PISOT} \left( 14,196\,k+47 \right) =[[14,196\,k+47,2744\,{k}^{2}+ 1316\,k+158,38416\,{k}^{3}+27636\,{k}^{2}+6633\,k+531,537824\,{k}^{4}+ 515872\,{k}^{3}+185682\,{k}^{2}+29720\,k+1785],[4+14\,k,-2-9\,k,-1-2\,k ,2+7\,k,-1-4\,k]] {\it PISOT} \left( 14,196\,k+48 \right) =[[14,196\,k+48,2744\,{k}^{2}+ 1344\,k+165,38416\,{k}^{3}+28224\,{k}^{2}+6924\,k+567],[3+14\,k,1+6\,k, 2+7\,k,-1-4\,k]] {\it PISOT} \left( 14,196\,k+49 \right) =[[14,196\,k+49,2744\,{k}^{2}+ 1372\,k+172],[4+14\,k,-2-7\,k,1+4\,k]] {\it PISOT} \left( 14,196\,k+50 \right) =[[14,196\,k+50,2744\,{k}^{2}+ 1400\,k+179,38416\,{k}^{3}+29400\,{k}^{2}+7512\,k+641],[3+14\,k,2+8\,k, k,1+4\,k]] {\it PISOT} \left( 14,196\,k+51 \right) =[[14,196\,k+51,2744\,{k}^{2}+ 1428\,k+186,38416\,{k}^{3}+29988\,{k}^{2}+7809\,k+678],[3+14\,k,2+9\,k, 1+5\,k,1+4\,k]] {\it PISOT} \left( 14,196\,k+53 \right) =[[14,196\,k+53],[3+14\,k,3+11 \,k]] {\it PISOT} \left( 14,196\,k+59 \right) =[[14,196\,k+59,2744\,{k}^{2}+ 1652\,k+249],[5+14\,k,-4-11\,k,3+10\,k]] {\it PISOT} \left( 14,196\,k+60 \right) =[[14,196\,k+60,2744\,{k}^{2}+ 1680\,k+257],[5+14\,k,-4-10\,k,4+13\,k]] {\it PISOT} \left( 14,196\,k+63 \right) =[[14,196\,k+63,2744\,{k}^{2}+ 1764\,k+284],[5+14\,k,-2-7\,k,-1-3\,k]] {\it PISOT} \left( 14,196\,k+65 \right) =[[14,196\,k+65],[4+14\,k,3+9\, k]] {\it PISOT} \left( 14,196\,k+66 \right) =[[14,196\,k+66,2744\,{k}^{2}+ 1848\,k+311],[5+14\,k,-2-4\,k,3+9\,k]] {\it PISOT} \left( 14,196\,k+67 \right) =[[14,196\,k+67],[5+14\,k,-1-3 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998961284771711 {\it PISOT} \left( 14,196\,k+68 \right) =[[14,196\,k+68,2744\,{k}^{2}+ 1904\,k+330,38416\,{k}^{3}+39984\,{k}^{2}+13864\,k+1601,537824\,{k}^{4} +746368\,{k}^{3}+388248\,{k}^{2}+89708\,k+7767],[4+14\,k,4+12\,k,1+2\,k ,-2-5\,k,1+3\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.981668422482757 {\it PISOT} \left( 14,196\,k+71 \right) =[[14,196\,k+71,2744\,{k}^{2}+ 1988\,k+360,38416\,{k}^{3}+41748\,{k}^{2}+15121\,k+1825],[5+14\,k,k,1+5 \,k,4+11\,k]] {\it PISOT} \left( 14,196\,k+75 \right) =[[14,196\,k+75,2744\,{k}^{2}+ 2100\,k+402],[5+14\,k,1+5\,k,5+13\,k]] {\it PISOT} \left( 14,196\,k+77 \right) =[[14,196\,k+77,2744\,{k}^{2}+ 2156\,k+424,38416\,{k}^{3}+45276\,{k}^{2}+17801\,k+2335],[5+14\,k,2+7\, k,4+11\,k,2+5\,k]] {\it PISOT} \left( 14,196\,k+78 \right) =[[14,196\,k+78,2744\,{k}^{2}+ 2184\,k+435],[6+14\,k,-2-6\,k,-2-5\,k]] {\it PISOT} \left( 14,196\,k+79 \right) =[[14,196\,k+79],[6+14\,k,-2-5 \,k]] {\it PISOT} \left( 14,196\,k+82 \right) =[[14,196\,k+82],[5+14\,k,5+12 \,k]] {\it PISOT} \left( 14,196\,k+83 \right) =[[14,196\,k+83,2744\,{k}^{2}+ 2324\,k+492,38416\,{k}^{3}+48804\,{k}^{2}+20665\,k+2916,537824\,{k}^{4} +911008\,{k}^{3}+578634\,{k}^{2}+163320\,k+17283],[5+14\,k,5+13\,k,2+7 \,k,5+13\,k,3+7\,k]] {\it PISOT} \left( 14,196\,k+85 \right) =[[14,196\,k+85,2744\,{k}^{2}+ 2380\,k+516],[5+14\,k,6+15\,k,3+7\,k]] {\it PISOT} \left( 14,196\,k+87 \right) =[[14,196\,k+87,2744\,{k}^{2}+ 2436\,k+541],[6+14\,k,2+3\,k,-4-9\,k]] {\it PISOT} \left( 14,196\,k+88 \right) =[[14,196\,k+88,2744\,{k}^{2}+ 2464\,k+553,38416\,{k}^{3}+51744\,{k}^{2}+23228\,k+3475,537824\,{k}^{4} +965888\,{k}^{3}+650412\,{k}^{2}+194628\,k+21837],[7+14\,k,-5-10\,k,4+7 \,k,-6-12\,k,4+9\,k]] {\it PISOT} \left( 14,196\,k+96 \right) =[[14,196\,k+96],[7+14\,k,-1-2 \,k]] {\it PISOT} \left( 14,196\,k+97 \right) =[[14,196\,k+97,2744\,{k}^{2}+ 2716\,k+672],[6+14\,k,6+13\,k,3+6\,k]] {\it PISOT} \left( 14,196\,k+99 \right) =[[14,196\,k+99,2744\,{k}^{2}+ 2772\,k+700],[8+14\,k,-7-13\,k,3+6\,k]] {\it PISOT} \left( 14,196\,k+100 \right) =[[14,196\,k+100],[7+14\,k,1+2 \,k]] {\it PISOT} \left( 14,196\,k+108 \right) =[[14,196\,k+108,2744\,{k}^{2} +3024\,k+833,38416\,{k}^{3}+63504\,{k}^{2}+34988\,k+6425,537824\,{k}^{4 }+1185408\,{k}^{3}+979692\,{k}^{2}+359828\,k+49557],[7+14\,k,5+10\,k,3+ 7\,k,6+12\,k,5+9\,k]] {\it PISOT} \left( 14,196\,k+109 \right) =[[14,196\,k+109,2744\,{k}^{2} +3052\,k+849],[8+14\,k,-1-3\,k,-5-9\,k]] {\it PISOT} \left( 14,196\,k+111 \right) =[[14,196\,k+111,2744\,{k}^{2} +3108\,k+880],[9+14\,k,-9-15\,k,4+7\,k]] {\it PISOT} \left( 14,196\,k+113 \right) =[[14,196\,k+113,2744\,{k}^{2} +3164\,k+912,38416\,{k}^{3}+66444\,{k}^{2}+38305\,k+7361,537824\,{k}^{4 }+1240288\,{k}^{3}+1072554\,{k}^{2}+412220\,k+59413],[9+14\,k,-8-13\,k, 5+7\,k,-8-13\,k,4+7\,k]] {\it PISOT} \left( 14,196\,k+114 \right) =[[14,196\,k+114],[9+14\,k,-7- 12\,k]] {\it PISOT} \left( 14,196\,k+117 \right) =[[14,196\,k+117],[8+14\,k,3+5 \,k]] {\it PISOT} \left( 14,196\,k+118 \right) =[[14,196\,k+118,2744\,{k}^{2} +3304\,k+995],[8+14\,k,4+6\,k,-3-5\,k]] {\it PISOT} \left( 14,196\,k+119 \right) =[[14,196\,k+119,2744\,{k}^{2} +3332\,k+1012,38416\,{k}^{3}+69972\,{k}^{2}+42497\,k+8606],[9+14\,k,-5- 7\,k,7+11\,k,-3-5\,k]] {\it PISOT} \left( 14,196\,k+121 \right) =[[14,196\,k+121,2744\,{k}^{2} +3388\,k+1046],[9+14\,k,-4-5\,k,8+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.981668315388927 {\it PISOT} \left( 14,196\,k+125 \right) =[[14,196\,k+125,2744\,{k}^{2} +3500\,k+1116,38416\,{k}^{3}+73500\,{k}^{2}+46873\,k+9964],[9+14\,k,-1- k,4+5\,k,-7-11\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998962669113346 {\it PISOT} \left( 14,196\,k+128 \right) =[[14,196\,k+128,2744\,{k}^{2} +3584\,k+1170,38416\,{k}^{3}+75264\,{k}^{2}+49144\,k+10695,537824\,{k}^ {4}+1404928\,{k}^{3}+1376088\,{k}^{2}+598980\,k+97763],[10+14\,k,-8-12 \,k,1+2\,k,3+5\,k,2+3\,k]] {\it PISOT} \left( 14,196\,k+129 \right) =[[14,196\,k+129],[9+14\,k,2+3 \,k]] {\it PISOT} \left( 14,196\,k+130 \right) =[[14,196\,k+130,2744\,{k}^{2} +3640\,k+1207],[9+14\,k,2+4\,k,6+9\,k]] {\it PISOT} \left( 14,196\,k+131 \right) =[[14,196\,k+131],[10+14\,k,-6 -9\,k]] {\it PISOT} \left( 14,196\,k+133 \right) =[[14,196\,k+133,2744\,{k}^{2} +3724\,k+1264],[9+14\,k,5+7\,k,-2-3\,k]] {\it PISOT} \left( 14,196\,k+136 \right) =[[14,196\,k+136,2744\,{k}^{2} +3808\,k+1321],[9+14\,k,6+10\,k,9+13\,k]] {\it PISOT} \left( 14,196\,k+137 \right) =[[14,196\,k+137,2744\,{k}^{2} +3836\,k+1341],[9+14\,k,7+11\,k,7+10\,k]] {\it PISOT} \left( 14,196\,k+143 \right) =[[14,196\,k+143],[11+14\,k,-8 -11\,k]] {\it PISOT} \left( 14,196\,k+145 \right) =[[14,196\,k+145,2744\,{k}^{2} +4060\,k+1502,38416\,{k}^{3}+85260\,{k}^{2}+63081\,k+15559],[11+14\,k,- 7-9\,k,4+5\,k,-3-4\,k]] {\it PISOT} \left( 14,196\,k+146 \right) =[[14,196\,k+146,2744\,{k}^{2} +4088\,k+1523,38416\,{k}^{3}+85848\,{k}^{2}+63960\,k+15887],[11+14\,k,- 6-8\,k,1+k,-3-4\,k]] {\it PISOT} \left( 14,196\,k+147 \right) =[[14,196\,k+147,2744\,{k}^{2} +4116\,k+1544],[10+14\,k,5+7\,k,3+4\,k]] {\it PISOT} \left( 14,196\,k+148 \right) =[[14,196\,k+148,2744\,{k}^{2} +4144\,k+1565,38416\,{k}^{3}+87024\,{k}^{2}+65724\,k+16549],[11+14\,k,- 5-6\,k,5+7\,k,3+4\,k]] {\it PISOT} \left( 14,196\,k+149 \right) =[[14,196\,k+149,2744\,{k}^{2} +4172\,k+1586,38416\,{k}^{3}+87612\,{k}^{2}+66609\,k+16882,537824\,{k}^ {4}+1635424\,{k}^{3}+1865010\,{k}^{2}+945324\,k+179699],[10+14\,k,7+9\, k,-1-2\,k,-5-7\,k,-3-4\,k]] {\it PISOT} \left( 14,196\,k+151 \right) =[[14,196\,k+151,2744\,{k}^{2} +4228\,k+1629],[12+14\,k,-14-17\,k,10+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.982982091476034 {\it PISOT} \left( 14,196\,k+152 \right) =[[14,196\,k+152,2744\,{k}^{2} +4256\,k+1650,38416\,{k}^{3}+89376\,{k}^{2}+69304\,k+17911],[11+14\,k,- 2-2\,k,4+6\,k,7+9\,k]] {\it PISOT} \left( 14,196\,k+153 \right) =[[14,196\,k+153,2744\,{k}^{2} +4284\,k+1672,38416\,{k}^{3}+89964\,{k}^{2}+70225\,k+18272],[11+14\,k,- 1-k,3+3\,k,-7-9\,k]] {\it PISOT} \left( 14,196\,k+156 \right) =[[14,196\,k+156,2744\,{k}^{2} +4368\,k+1738,38416\,{k}^{3}+91728\,{k}^{2}+73000\,k+19363],[11+14\,k,1 +2\,k,6+8\,k,4+5\,k]] {\it PISOT} \left( 14,196\,k+157 \right) =[[14,196\,k+157,2744\,{k}^{2} +4396\,k+1761,38416\,{k}^{3}+92316\,{k}^{2}+73957\,k+19752],[12+14\,k,- 9-11\,k,2+3\,k,4+5\,k]] {\it PISOT} \left( 14,196\,k+158 \right) =[[14,196\,k+158,2744\,{k}^{2} +4424\,k+1783,38416\,{k}^{3}+92904\,{k}^{2}+74888\,k+20121,537824\,{k}^ {4}+1734208\,{k}^{3}+2096892\,{k}^{2}+1126816\,k+227064],[12+14\,k,-9- 10\,k,11+13\,k,-6-7\,k,4+5\,k]] {\it PISOT} \left( 14,196\,k+161 \right) =[[14,196\,k+161,2744\,{k}^{2} +4508\,k+1852],[13+14\,k,-18-21\,k,9+11\,k]] {\it PISOT} \left( 14,196\,k+163 \right) =[[14,196\,k+163,2744\,{k}^{2} +4564\,k+1898],[12+14\,k,-5-5\,k,10+12\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.991479183467174 {\it PISOT} \left( 14,196\,k+165 \right) =[[14,196\,k+165,2744\,{k}^{2} +4620\,k+1945,38416\,{k}^{3}+97020\,{k}^{2}+81685\,k+22927,537824\,{k}^ {4}+1811040\,{k}^{3}+2287110\,{k}^{2}+1283806\,k+270256,7529536\,{k}^{5 }+31693200\,{k}^{4}+53364920\,{k}^{3}+44930901\,{k}^{2}+18916103\,k+ 3185690],[11+14\,k,9+11\,k,3+4\,k,4+5\,k,3+3\,k,-5-6\,k]] {\it PISOT} \left( 14,196\,k+167 \right) =[[14,196\,k+167,2744\,{k}^{2} +4676\,k+1992,38416\,{k}^{3}+98196\,{k}^{2}+83665\,k+23761],[13+14\,k,- 14-15\,k,15+17\,k,-6-7\,k]] {\it PISOT} \left( 14,196\,k+177 \right) =[[14,196\,k+177,2744\,{k}^{2} +4956\,k+2238,38416\,{k}^{3}+104076\,{k}^{2}+93993\,k+28297],[13+14\,k, -5-5\,k,7+7\,k,-9-10\,k]] {\it PISOT} \left( 14,196\,k+180 \right) =[[14,196\,k+180],[12+14\,k,11 +12\,k]] {\it PISOT} \left( 14,196\,k+181 \right) =[[14,196\,k+181],[12+14\,k,12 +13\,k]] {\it PISOT} \left( 14,196\,k+188 \right) =[[14,196\,k+188,2744\,{k}^{2} +5264\,k+2525,38416\,{k}^{3}+110544\,{k}^{2}+106044\,k+33913,537824\,{k }^{4}+2063488\,{k}^{3}+2969148\,{k}^{2}+1898964\,k+455482,7529536\,{k}^ {5}+36111040\,{k}^{4}+69278944\,{k}^{3}+66460316\,{k}^{2}+31880409\,k+ 6117532],[13+14\,k,6+6\,k,-3-3\,k,2+2\,k,-1-k,1+k]] {\it PISOT} \left( 14,196\,k+189 \right) =[[14,196\,k+189,2744\,{k}^{2} +5292\,k+2552,38416\,{k}^{3}+111132\,{k}^{2}+107177\,k+34459,537824\,{k }^{4}+2074464\,{k}^{3}+3000858\,{k}^{2}+1929508\,k+465291],[14+14\,k,-7 -7\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 14,196\,k+190 \right) =[[14,196\,k+190,2744\,{k}^{2} +5320\,k+2579,38416\,{k}^{3}+111720\,{k}^{2}+108312\,k+35007],[14+14\,k ,-6-6\,k,3+3\,k,-1-k]] {\it PISOT} \left( 14,196\,k+191 \right) =[[14,196\,k+191,2744\,{k}^{2} +5348\,k+2606,38416\,{k}^{3}+112308\,{k}^{2}+109449\,k+35556],[14+14\,k ,-5-5\,k,2+2\,k,-1-k]] {\it PISOT} \left( 14,196\,k+192 \right) =[[14,196\,k+192,2744\,{k}^{2} +5376\,k+2633],[14+14\,k,-4-4\,k,1+k]] {\it PISOT} \left( 14,196\,k+193 \right) =[[14,196\,k+193,2744\,{k}^{2} +5404\,k+2661],[14+14\,k,-3-3\,k,1+k]] {\it PISOT} \left( 14,196\,k+194 \right) =[[14,196\,k+194],[14+14\,k,-2 -2\,k]] {\it PISOT} \left( 14,196\,k+195 \right) =[[14,196\,k+195],[14+14\,k,-1 -k]] {\it PISOT} \left( 15,225\,k+1 \right) =[[15,225\,k+1],[15\,k,k]] {\it PISOT} \left( 15,225\,k+2 \right) =[[15,225\,k+2],[15\,k,2\,k]] {\it PISOT} \left( 15,225\,k+3 \right) =[[15,225\,k+3,3375\,{k}^{2}+90 \,k+1],[15\,k,3\,k,k]] {\it PISOT} \left( 15,225\,k+4 \right) =[[15,225\,k+4,3375\,{k}^{2}+120 \,k+1],[15\,k,4\,k,k]] {\it PISOT} \left( 15,225\,k+5 \right) =[[15,225\,k+5,3375\,{k}^{2}+150 \,k+2,50625\,{k}^{3}+3375\,{k}^{2}+85\,k+1],[15\,k,5\,k,2\,k,k]] {\it PISOT} \left( 15,225\,k+6 \right) =[[15,225\,k+6,3375\,{k}^{2}+180 \,k+2,50625\,{k}^{3}+4050\,{k}^{2}+96\,k+1],[15\,k,6\,k,2\,k,k]] {\it PISOT} \left( 15,225\,k+7 \right) =[[15,225\,k+7,3375\,{k}^{2}+210 \,k+3,50625\,{k}^{3}+4725\,{k}^{2}+139\,k+1],[15\,k,7\,k,3\,k,k]] {\it PISOT} \left( 15,225\,k+8 \right) =[[15,225\,k+8,3375\,{k}^{2}+240 \,k+4,50625\,{k}^{3}+5400\,{k}^{2}+184\,k+2,759375\,{k}^{4}+108000\,{k} ^{3}+5580\,{k}^{2}+124\,k+1],[15\,k,8\,k,4\,k,2\,k,k]] {\it PISOT} \left( 15,225\,k+9 \right) =[[15,225\,k+9,3375\,{k}^{2}+270 \,k+5,50625\,{k}^{3}+6075\,{k}^{2}+231\,k+3,759375\,{k}^{4}+121500\,{k} ^{3}+7020\,{k}^{2}+180\,k+2,11390625\,{k}^{5}+2278125\,{k}^{4}+176850\, {k}^{3}+6804\,{k}^{2}+139\,k+1],[15\,k,9\,k,5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 15,225\,k+16 \right) =[[15,225\,k+16],[2+15\,k,-1-14 \,k]] {\it PISOT} \left( 15,225\,k+17 \right) =[[15,225\,k+17],[2+15\,k,-1-13 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.978222659277365 {\it PISOT} \left( 15,225\,k+20 \right) =[[15,225\,k+20,3375\,{k}^{2}+ 600\,k+27,50625\,{k}^{3}+13500\,{k}^{2}+1210\,k+36],[1+15\,k,1+5\,k,-8 \,k,-1-11\,k]] {\it PISOT} \left( 15,225\,k+21 \right) =[[15,225\,k+21,3375\,{k}^{2}+ 630\,k+29,50625\,{k}^{3}+14175\,{k}^{2}+1311\,k+40],[1+15\,k,6\,k,8\,k, 1+11\,k]] {\it PISOT} \left( 15,225\,k+22 \right) =[[15,225\,k+22,3375\,{k}^{2}+ 660\,k+32],[1+15\,k,7\,k,1+10\,k]] {\it PISOT} \left( 15,225\,k+28 \right) =[[15,225\,k+28,3375\,{k}^{2}+ 840\,k+52,50625\,{k}^{3}+18900\,{k}^{2}+2344\,k+97],[2+15\,k,-2\,k,-1-4 \,k,1+8\,k]] {\it PISOT} \left( 15,225\,k+29 \right) =[[15,225\,k+29,3375\,{k}^{2}+ 870\,k+56,50625\,{k}^{3}+19575\,{k}^{2}+2521\,k+108],[1+15\,k,1+14\,k,1 +12\,k,1+8\,k]] {\it PISOT} \left( 15,225\,k+31 \right) =[[15,225\,k+31,3375\,{k}^{2}+ 930\,k+64,50625\,{k}^{3}+20925\,{k}^{2}+2881\,k+132,759375\,{k}^{4}+ 418500\,{k}^{3}+86445\,{k}^{2}+7928\,k+272],[2+15\,k,k,2\,k,1+4\,k,-1-7 \,k]] {\it PISOT} \left( 15,225\,k+32 \right) =[[15,225\,k+32,3375\,{k}^{2}+ 960\,k+68,50625\,{k}^{3}+21600\,{k}^{2}+3064\,k+144],[2+15\,k,2\,k,1+4 \,k,-1-7\,k]] {\it PISOT} \left( 15,225\,k+33 \right) =[[15,225\,k+33,3375\,{k}^{2}+ 990\,k+73],[2+15\,k,3\,k,1+7\,k]] {\it PISOT} \left( 15,225\,k+38 \right) =[[15,225\,k+38,3375\,{k}^{2}+ 1140\,k+96,50625\,{k}^{3}+25650\,{k}^{2}+4324\,k+243,759375\,{k}^{4}+ 513000\,{k}^{3}+129780\,{k}^{2}+14586\,k+615],[3+15\,k,-1-7\,k,-3\,k,-2 -7\,k,2+12\,k]] {\it PISOT} \left( 15,225\,k+41 \right) =[[15,225\,k+41],[2+15\,k,2+11 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.973283997673568 {\it PISOT} \left( 15,225\,k+44 \right) =[[15,225\,k+44,3375\,{k}^{2}+ 1320\,k+129,50625\,{k}^{3}+29700\,{k}^{2}+5806\,k+378],[3+15\,k,-1-k,2+ 12\,k,1+5\,k]] {\it PISOT} \left( 15,225\,k+54 \right) =[[15,225\,k+54,3375\,{k}^{2}+ 1620\,k+194,50625\,{k}^{3}+36450\,{k}^{2}+8736\,k+697,759375\,{k}^{4}+ 729000\,{k}^{3}+262170\,{k}^{2}+41862\,k+2504,11390625\,{k}^{5}+ 13668750\,{k}^{4}+6555600\,{k}^{3}+1570779\,{k}^{2}+188032\,k+8996],[4+ 15\,k,-1-6\,k,-2-7\,k,1+5\,k,1+3\,k,-1-4\,k]] {\it PISOT} \left( 15,225\,k+55 \right) =[[15,225\,k+55,3375\,{k}^{2}+ 1650\,k+202,50625\,{k}^{3}+37125\,{k}^{2}+9085\,k+742],[4+15\,k,-1-5\,k ,-1-3\,k,1+4\,k]] {\it PISOT} \left( 15,225\,k+56 \right) =[[15,225\,k+56],[4+15\,k,-1-4 \,k]] {\it PISOT} \left( 15,225\,k+57 \right) =[[15,225\,k+57,3375\,{k}^{2}+ 1710\,k+217],[4+15\,k,-1-3\,k,1+4\,k]] {\it PISOT} \left( 15,225\,k+58 \right) =[[15,225\,k+58,3375\,{k}^{2}+ 1740\,k+224,50625\,{k}^{3}+39150\,{k}^{2}+10084\,k+865],[3+15\,k,3+13\, k,1+5\,k,1+4\,k]] {\it PISOT} \left( 15,225\,k+61 \right) =[[15,225\,k+61,3375\,{k}^{2}+ 1830\,k+248],[4+15\,k,1+k,-3-11\,k]] {\it PISOT} \left( 15,225\,k+64 \right) =[[15,225\,k+64,3375\,{k}^{2}+ 1920\,k+273,50625\,{k}^{3}+43200\,{k}^{2}+12286\,k+1165],[5+15\,k,-3-11 \,k,-1-2\,k,2+7\,k]] {\it PISOT} \left( 15,225\,k+65 \right) =[[15,225\,k+65,3375\,{k}^{2}+ 1950\,k+282],[4+15\,k,1+5\,k,2+7\,k]] {\it PISOT} \left( 15,225\,k+72 \right) =[[15,225\,k+72,3375\,{k}^{2}+ 2160\,k+346,50625\,{k}^{3}+48600\,{k}^{2}+15564\,k+1663],[4+15\,k,3+12 \,k,4+13\,k,1+3\,k]] {\it PISOT} \left( 15,225\,k+73 \right) =[[15,225\,k+73,3375\,{k}^{2}+ 2190\,k+355,50625\,{k}^{3}+49275\,{k}^{2}+15979\,k+1726,759375\,{k}^{4} +985500\,{k}^{3}+479430\,{k}^{2}+103610\,k+8392,11390625\,{k}^{5}+ 18478125\,{k}^{4}+11986650\,{k}^{3}+3886417\,{k}^{2}+629781\,k+40803],[ 4+15\,k,3+13\,k,5+18\,k,3+12\,k,4+13\,k,1+3\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.971994603480665 {\it PISOT} \left( 15,225\,k+74 \right) =[[15,225\,k+74,3375\,{k}^{2}+ 2220\,k+365,50625\,{k}^{3}+49950\,{k}^{2}+16426\,k+1800,759375\,{k}^{4} +999000\,{k}^{3}+492795\,{k}^{2}+108020\,k+8877,11390625\,{k}^{5}+ 18731250\,{k}^{4}+12320100\,{k}^{3}+4051124\,{k}^{2}+665935\,k+43778],[ 5+15\,k,-1-k,3+10\,k,1+4\,k,1+5\,k,3+9\,k]] {\it PISOT} \left( 15,225\,k+76 \right) =[[15,225\,k+76,3375\,{k}^{2}+ 2280\,k+385],[4+15\,k,5+16\,k,2+6\,k]] {\it PISOT} \left( 15,225\,k+78 \right) =[[15,225\,k+78,3375\,{k}^{2}+ 2340\,k+406,50625\,{k}^{3}+52650\,{k}^{2}+18264\,k+2113,759375\,{k}^{4} +1053000\,{k}^{3}+547830\,{k}^{2}+126726\,k+10997,11390625\,{k}^{5}+ 19743750\,{k}^{4}+13694400\,{k}^{3}+4750947\,{k}^{2}+824374\,k+57233],[ 5+15\,k,1+3\,k,k,1+5\,k,4+11\,k,-1-3\,k]] {\it PISOT} \left( 15,225\,k+82 \right) =[[15,225\,k+82,3375\,{k}^{2}+ 2460\,k+448,50625\,{k}^{3}+55350\,{k}^{2}+20164\,k+2448,759375\,{k}^{4} +1107000\,{k}^{3}+604980\,{k}^{2}+146912\,k+13377],[6+15\,k,-3-8\,k,1+k ,-4-9\,k,4+11\,k]] {\it PISOT} \left( 15,225\,k+84 \right) =[[15,225\,k+84,3375\,{k}^{2}+ 2520\,k+470,50625\,{k}^{3}+56700\,{k}^{2}+21156\,k+2630],[6+15\,k,-2-6 \,k,-2-4\,k,3+8\,k]] {\it PISOT} \left( 15,225\,k+85 \right) =[[15,225\,k+85,3375\,{k}^{2}+ 2550\,k+482,50625\,{k}^{3}+57375\,{k}^{2}+21685\,k+2733],[5+15\,k,3+10 \,k,4+12\,k,3+8\,k]] {\it PISOT} \left( 15,225\,k+87 \right) =[[15,225\,k+87,3375\,{k}^{2}+ 2610\,k+505],[6+15\,k,-2-3\,k,5+13\,k]] {\it PISOT} \left( 15,225\,k+91 \right) =[[15,225\,k+91,3375\,{k}^{2}+ 2730\,k+552],[7+15\,k,-6-14\,k,2+5\,k]] {\it PISOT} \left( 15,225\,k+95 \right) =[[15,225\,k+95,3375\,{k}^{2}+ 2850\,k+602],[5+15\,k,8+20\,k,3+7\,k]] {\it PISOT} \left( 15,225\,k+96 \right) =[[15,225\,k+96,3375\,{k}^{2}+ 2880\,k+614],[6+15\,k,3+6\,k,-3-7\,k]] {\it PISOT} \left( 15,225\,k+97 \right) =[[15,225\,k+97],[6+15\,k,3+7\, k]] {\it PISOT} \left( 15,225\,k+98 \right) =[[15,225\,k+98,3375\,{k}^{2}+ 2940\,k+640,50625\,{k}^{3}+66150\,{k}^{2}+28804\,k+4180],[6+15\,k,4+8\, k,-3-8\,k,-3-7\,k]] {\it PISOT} \left( 15,225\,k+99 \right) =[[15,225\,k+99,3375\,{k}^{2}+ 2970\,k+653,50625\,{k}^{3}+66825\,{k}^{2}+29391\,k+4307],[7+15\,k,-2-6 \,k,-5-10\,k,4+9\,k]] {\it PISOT} \left( 15,225\,k+102 \right) =[[15,225\,k+102,3375\,{k}^{2} +3060\,k+694,50625\,{k}^{3}+68850\,{k}^{2}+31224\,k+4722],[7+15\,k,-1-3 \,k,-3-5\,k,5+11\,k]] {\it PISOT} \left( 15,225\,k+109 \right) =[[15,225\,k+109,3375\,{k}^{2} +3270\,k+792,50625\,{k}^{3}+73575\,{k}^{2}+35641\,k+5755],[8+15\,k,-6- 11\,k,5+10\,k,-1-2\,k]] {\it PISOT} \left( 15,225\,k+112 \right) =[[15,225\,k+112],[8+15\,k,-4- 8\,k]] {\it PISOT} \left( 15,225\,k+113 \right) =[[15,225\,k+113],[7+15\,k,4+8 \,k]] {\it PISOT} \left( 15,225\,k+116 \right) =[[15,225\,k+116,3375\,{k}^{2} +3480\,k+897,50625\,{k}^{3}+78300\,{k}^{2}+40366\,k+6936],[7+15\,k,5+11 \,k,5+10\,k,1+2\,k]] {\it PISOT} \left( 15,225\,k+123 \right) =[[15,225\,k+123,3375\,{k}^{2} +3690\,k+1009,50625\,{k}^{3}+83025\,{k}^{2}+45399\,k+8277],[8+15\,k,2+3 \,k,-2-5\,k,-6-11\,k]] {\it PISOT} \left( 15,225\,k+126 \right) =[[15,225\,k+126,3375\,{k}^{2} +3780\,k+1058,50625\,{k}^{3}+85050\,{k}^{2}+47616\,k+8884],[8+15\,k,4+6 \,k,-5-10\,k,-5-9\,k]] {\it PISOT} \left( 15,225\,k+127 \right) =[[15,225\,k+127,3375\,{k}^{2} +3810\,k+1075,50625\,{k}^{3}+85725\,{k}^{2}+48379\,k+9099],[9+15\,k,-4- 8\,k,-5-8\,k,4+7\,k]] {\it PISOT} \left( 15,225\,k+128 \right) =[[15,225\,k+128],[9+15\,k,-4- 7\,k]] {\it PISOT} \left( 15,225\,k+129 \right) =[[15,225\,k+129,3375\,{k}^{2} +3870\,k+1109],[9+15\,k,-3-6\,k,-4-7\,k]] {\it PISOT} \left( 15,225\,k+130 \right) =[[15,225\,k+130,3375\,{k}^{2} +3900\,k+1127],[10+15\,k,-12-20\,k,4+7\,k]] {\it PISOT} \left( 15,225\,k+134 \right) =[[15,225\,k+134,3375\,{k}^{2} +4020\,k+1197],[8+15\,k,8+14\,k,3+5\,k]] {\it PISOT} \left( 15,225\,k+138 \right) =[[15,225\,k+138,3375\,{k}^{2} +4140\,k+1270],[9+15\,k,1+3\,k,8+13\,k]] {\it PISOT} \left( 15,225\,k+140 \right) =[[15,225\,k+140,3375\,{k}^{2} +4200\,k+1307,50625\,{k}^{3}+94500\,{k}^{2}+58810\,k+12202],[10+15\,k,- 7-10\,k,8+12\,k,-5-8\,k]] {\it PISOT} \left( 15,225\,k+141 \right) =[[15,225\,k+141,3375\,{k}^{2} +4230\,k+1325,50625\,{k}^{3}+95175\,{k}^{2}+59631\,k+12451],[9+15\,k,4+ 6\,k,-2-4\,k,-5-8\,k]] {\it PISOT} \left( 15,225\,k+143 \right) =[[15,225\,k+143,3375\,{k}^{2} +4290\,k+1363,50625\,{k}^{3}+96525\,{k}^{2}+61339\,k+12991,759375\,{k}^ {4}+1930500\,{k}^{3}+1840230\,{k}^{2}+779548\,k+123820],[9+15\,k,5+8\,k ,k,5+9\,k,7+11\,k]] {\it PISOT} \left( 15,225\,k+147 \right) =[[15,225\,k+147,3375\,{k}^{2} +4410\,k+1441,50625\,{k}^{3}+99225\,{k}^{2}+64839\,k+14126,759375\,{k}^ {4}+1984500\,{k}^{3}+1945080\,{k}^{2}+847434\,k+138476,11390625\,{k}^{5 }+37209375\,{k}^{4}+48625650\,{k}^{3}+31776003\,{k}^{2}+10383805\,k+ 1357469],[10+15\,k,-2-3\,k,1+k,-4-5\,k,7+11\,k,2+3\,k]] {\it PISOT} \left( 15,225\,k+149 \right) =[[15,225\,k+149,3375\,{k}^{2} +4470\,k+1480],[11+15\,k,-11-16\,k,4+6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.971994371934685 {\it PISOT} \left( 15,225\,k+151 \right) =[[15,225\,k+151,3375\,{k}^{2} +4530\,k+1520,50625\,{k}^{3}+101925\,{k}^{2}+68401\,k+15301,759375\,{k} ^{4}+2038500\,{k}^{3}+2052045\,{k}^{2}+918070\,k+154027,11390625\,{k}^{ 5}+38221875\,{k}^{4}+51301350\,{k}^{3}+34427926\,{k}^{2}+11552112\,k+ 1550508],[10+15\,k,k,7+10\,k,-3-4\,k,4+5\,k,-6-9\,k]] {\it PISOT} \left( 15,225\,k+152 \right) =[[15,225\,k+152,3375\,{k}^{2} +4560\,k+1540,50625\,{k}^{3}+102600\,{k}^{2}+69304\,k+15603,759375\,{k} ^{4}+2052000\,{k}^{3}+2079180\,{k}^{2}+936250\,k+158087,11390625\,{k}^{ 5}+38475000\,{k}^{4}+51980400\,{k}^{3}+35111033\,{k}^{2}+11857522\,k+ 1601711],[11+15\,k,-10-13\,k,13+18\,k,-9-12\,k,9+13\,k,-2-3\,k]] {\it PISOT} \left( 15,225\,k+153 \right) =[[15,225\,k+153,3375\,{k}^{2} +4590\,k+1561,50625\,{k}^{3}+103275\,{k}^{2}+70239\,k+15926],[11+15\,k, -9-12\,k,9+13\,k,-2-3\,k]] {\it PISOT} \left( 15,225\,k+160 \right) =[[15,225\,k+160,3375\,{k}^{2} +4800\,k+1707],[11+15\,k,-4-5\,k,5+7\,k]] {\it PISOT} \left( 15,225\,k+161 \right) =[[15,225\,k+161,3375\,{k}^{2} +4830\,k+1728,50625\,{k}^{3}+108675\,{k}^{2}+77761\,k+18546],[10+15\,k, 8+11\,k,-1-2\,k,-5-7\,k]] {\it PISOT} \left( 15,225\,k+164 \right) =[[15,225\,k+164,3375\,{k}^{2} +4920\,k+1793],[11+15\,k,-k,-8-11\,k]] {\it PISOT} \left( 15,225\,k+167 \right) =[[15,225\,k+167,3375\,{k}^{2} +5010\,k+1859,50625\,{k}^{3}+112725\,{k}^{2}+83659\,k+20694],[12+15\,k, -10-13\,k,4+5\,k,-3-4\,k]] {\it PISOT} \left( 15,225\,k+168 \right) =[[15,225\,k+168,3375\,{k}^{2} +5040\,k+1882],[11+15\,k,2+3\,k,3+4\,k]] {\it PISOT} \left( 15,225\,k+169 \right) =[[15,225\,k+169],[11+15\,k,3+ 4\,k]] {\it PISOT} \left( 15,225\,k+170 \right) =[[15,225\,k+170,3375\,{k}^{2} +5100\,k+1927,50625\,{k}^{3}+114750\,{k}^{2}+86710\,k+21843],[11+15\,k, 4+5\,k,-2-3\,k,-3-4\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.973283662109210 {\it PISOT} \left( 15,225\,k+181 \right) =[[15,225\,k+181,3375\,{k}^{2} +5430\,k+2184,50625\,{k}^{3}+122175\,{k}^{2}+98281\,k+26353],[12+15\,k, k,10+12\,k,-4-5\,k]] {\it PISOT} \left( 15,225\,k+184 \right) =[[15,225\,k+184],[13+15\,k,-9 -11\,k]] {\it PISOT} \left( 15,225\,k+187 \right) =[[15,225\,k+187,3375\,{k}^{2} +5610\,k+2331,50625\,{k}^{3}+126225\,{k}^{2}+104899\,k+29056,759375\,{k }^{4}+2524500\,{k}^{3}+3147030\,{k}^{2}+1743474\,k+362184],[12+15\,k,6+ 7\,k,-3-3\,k,5+7\,k,10+12\,k]] {\it PISOT} \left( 15,225\,k+192 \right) =[[15,225\,k+192,3375\,{k}^{2} +5760\,k+2458],[13+15\,k,-3-3\,k,6+7\,k]] {\it PISOT} \left( 15,225\,k+193 \right) =[[15,225\,k+193,3375\,{k}^{2} +5790\,k+2483,50625\,{k}^{3}+130275\,{k}^{2}+111739\,k+31945],[13+15\,k ,-2-2\,k,3+4\,k,6+7\,k]] {\it PISOT} \left( 15,225\,k+194 \right) =[[15,225\,k+194,3375\,{k}^{2} +5820\,k+2509,50625\,{k}^{3}+130950\,{k}^{2}+112906\,k+32449,759375\,{k }^{4}+2619000\,{k}^{3}+3387195\,{k}^{2}+1946962\,k+419664],[13+15\,k,-1 -k,2+2\,k,-3-4\,k,-6-7\,k]] {\it PISOT} \left( 15,225\,k+196 \right) =[[15,225\,k+196,3375\,{k}^{2} +5880\,k+2561,50625\,{k}^{3}+132300\,{k}^{2}+115246\,k+33463],[14+15\,k ,-13-14\,k,11+12\,k,-7-8\,k]] {\it PISOT} \left( 15,225\,k+197 \right) =[[15,225\,k+197,3375\,{k}^{2} +5910\,k+2587,50625\,{k}^{3}+132975\,{k}^{2}+116419\,k+33972],[13+15\,k ,2+2\,k,-3-4\,k,-7-8\,k]] {\it PISOT} \left( 15,225\,k+203 \right) =[[15,225\,k+203,3375\,{k}^{2} +6090\,k+2747],[14+15\,k,-7-7\,k,9+10\,k]] {\it PISOT} \left( 15,225\,k+204 \right) =[[15,225\,k+204,3375\,{k}^{2} +6120\,k+2774,50625\,{k}^{3}+137700\,{k}^{2}+124836\,k+37721],[14+15\,k ,-6-6\,k,8+8\,k,-10-11\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.978221647569147 {\it PISOT} \left( 15,225\,k+205 \right) =[[15,225\,k+205,3375\,{k}^{2} +6150\,k+2802,50625\,{k}^{3}+138375\,{k}^{2}+126085\,k+38299],[14+15\,k ,-4-5\,k,-8-8\,k,10+11\,k]] {\it PISOT} \left( 15,225\,k+208 \right) =[[15,225\,k+208],[13+15\,k,12 +13\,k]] {\it PISOT} \left( 15,225\,k+209 \right) =[[15,225\,k+209],[13+15\,k,13 +14\,k]] {\it PISOT} \left( 15,225\,k+216 \right) =[[15,225\,k+216,3375\,{k}^{2} +6480\,k+3110,50625\,{k}^{3}+145800\,{k}^{2}+139956\,k+44778,759375\,{k }^{4}+2916000\,{k}^{3}+4198770\,{k}^{2}+2686860\,k+644717,11390625\,{k} ^{5}+54675000\,{k}^{4}+104970600\,{k}^{3}+100761246\,{k}^{2}+48357706\, k+9282684],[15+15\,k,-9-9\,k,5+5\,k,-3-3\,k,2+2\,k,-1-k]] {\it PISOT} \left( 15,225\,k+217 \right) =[[15,225\,k+217,3375\,{k}^{2} +6510\,k+3139,50625\,{k}^{3}+146475\,{k}^{2}+141259\,k+45407,759375\,{k }^{4}+2929500\,{k}^{3}+4237830\,{k}^{2}+2724536\,k+656832],[15+15\,k,-8 -8\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 15,225\,k+218 \right) =[[15,225\,k+218,3375\,{k}^{2} +6540\,k+3168,50625\,{k}^{3}+147150\,{k}^{2}+142564\,k+46038],[15+15\,k ,-7-7\,k,3+3\,k,-1-k]] {\it PISOT} \left( 15,225\,k+219 \right) =[[15,225\,k+219,3375\,{k}^{2} +6570\,k+3197,50625\,{k}^{3}+147825\,{k}^{2}+143871\,k+46670],[15+15\,k ,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 15,225\,k+220 \right) =[[15,225\,k+220,3375\,{k}^{2} +6600\,k+3227,50625\,{k}^{3}+148500\,{k}^{2}+145210\,k+47334],[15+15\,k ,-5-5\,k,2+2\,k,-1-k]] {\it PISOT} \left( 15,225\,k+221 \right) =[[15,225\,k+221,3375\,{k}^{2} +6630\,k+3256],[15+15\,k,-4-4\,k,1+k]] {\it PISOT} \left( 15,225\,k+222 \right) =[[15,225\,k+222,3375\,{k}^{2} +6660\,k+3286],[15+15\,k,-3-3\,k,1+k]] {\it PISOT} \left( 15,225\,k+223 \right) =[[15,225\,k+223],[15+15\,k,-2 -2\,k]] {\it PISOT} \left( 15,225\,k+224 \right) =[[15,225\,k+224],[15+15\,k,-1 -k]] {\it PISOT} \left( 16,256\,k+1 \right) =[[16,256\,k+1],[16\,k,k]] {\it PISOT} \left( 16,256\,k+2 \right) =[[16,256\,k+2],[16\,k,2\,k]] {\it PISOT} \left( 16,256\,k+3 \right) =[[16,256\,k+3,4096\,{k}^{2}+96 \,k+1],[16\,k,3\,k,k]] {\it PISOT} \left( 16,256\,k+4 \right) =[[16,256\,k+4,4096\,{k}^{2}+128 \,k+1],[16\,k,4\,k,k]] {\it PISOT} \left( 16,256\,k+5 \right) =[[16,256\,k+5,4096\,{k}^{2}+160 \,k+2,65536\,{k}^{3}+3840\,{k}^{2}+89\,k+1],[16\,k,5\,k,2\,k,k]] {\it PISOT} \left( 16,256\,k+6 \right) =[[16,256\,k+6,4096\,{k}^{2}+192 \,k+2,65536\,{k}^{3}+4608\,{k}^{2}+100\,k+1],[16\,k,6\,k,2\,k,k]] {\it PISOT} \left( 16,256\,k+7 \right) =[[16,256\,k+7,4096\,{k}^{2}+224 \,k+3,65536\,{k}^{3}+5376\,{k}^{2}+145\,k+1],[16\,k,7\,k,3\,k,k]] {\it PISOT} \left( 16,256\,k+8 \right) =[[16,256\,k+8,4096\,{k}^{2}+256 \,k+4,65536\,{k}^{3}+6144\,{k}^{2}+192\,k+2,1048576\,{k}^{4}+131072\,{k }^{3}+6144\,{k}^{2}+128\,k+1],[1+16\,k,-8\,k,-4\,k,-2\,k,-k]] {\it PISOT} \left( 16,256\,k+9 \right) =[[16,256\,k+9,4096\,{k}^{2}+288 \,k+5,65536\,{k}^{3}+6912\,{k}^{2}+241\,k+3,1048576\,{k}^{4}+147456\,{k }^{3}+7728\,{k}^{2}+186\,k+2,16777216\,{k}^{5}+2949120\,{k}^{4}+206336 \,{k}^{3}+7353\,{k}^{2}+143\,k+1],[16\,k,9\,k,5\,k,3\,k,2\,k,k]] {\it PISOT} \left( 16,256\,k+17 \right) =[[16,256\,k+17],[2+16\,k,-1-15 \,k]] {\it PISOT} \left( 16,256\,k+18 \right) =[[16,256\,k+18],[2+16\,k,-1-14 \,k]] {\it PISOT} \left( 16,256\,k+21 \right) =[[16,256\,k+21,4096\,{k}^{2}+ 672\,k+28],[16\,k,1+21\,k,1+12\,k]] {\it PISOT} \left( 16,256\,k+25 \right) =[[16,256\,k+25,4096\,{k}^{2}+ 800\,k+39,65536\,{k}^{3}+19200\,{k}^{2}+1873\,k+61,1048576\,{k}^{4}+ 409600\,{k}^{3}+59952\,{k}^{2}+3902\,k+95,16777216\,{k}^{5}+8192000\,{k }^{4}+1598976\,{k}^{3}+156073\,{k}^{2}+7611\,k+148],[2+16\,k,-1-7\,k,5 \,k,1+8\,k,-1-4\,k,1+10\,k]] {\it PISOT} \left( 16,256\,k+26 \right) =[[16,256\,k+26],[1+16\,k,1+10 \,k]] {\it PISOT} \left( 16,256\,k+28 \right) =[[16,256\,k+28,4096\,{k}^{2}+ 896\,k+49],[2+16\,k,-1-4\,k,1+9\,k]] {\it PISOT} \left( 16,256\,k+31 \right) =[[16,256\,k+31,4096\,{k}^{2}+ 992\,k+60,65536\,{k}^{3}+23808\,{k}^{2}+2881\,k+116,1048576\,{k}^{4}+ 507904\,{k}^{3}+92208\,{k}^{2}+7432\,k+224],[2+16\,k,-k,-2\,k,-1-4\,k,1 +8\,k]] {\it PISOT} \left( 16,256\,k+33 \right) =[[16,256\,k+33,4096\,{k}^{2}+ 1056\,k+68,65536\,{k}^{3}+25344\,{k}^{2}+3265\,k+140,1048576\,{k}^{4}+ 540672\,{k}^{3}+104496\,{k}^{2}+8968\,k+288],[2+16\,k,k,2\,k,4\,k,1+8\, k]] {\it PISOT} \left( 16,256\,k+35 \right) =[[16,256\,k+35,4096\,{k}^{2}+ 1120\,k+77,65536\,{k}^{3}+26880\,{k}^{2}+3689\,k+169,1048576\,{k}^{4}+ 573440\,{k}^{3}+117936\,{k}^{2}+10798\,k+371,16777216\,{k}^{5}+11468800 \,{k}^{4}+3143168\,{k}^{3}+431387\,{k}^{2}+29631\,k+814],[1+16\,k,2+19 \,k,1+10\,k,1+6\,k,-3\,k,-1-7\,k]] {\it PISOT} \left( 16,256\,k+36 \right) =[[16,256\,k+36,4096\,{k}^{2}+ 1152\,k+81],[2+16\,k,1+4\,k,-1-7\,k]] {\it PISOT} \left( 16,256\,k+37 \right) =[[16,256\,k+37,4096\,{k}^{2}+ 1184\,k+86],[3+16\,k,-2-11\,k,1+7\,k]] {\it PISOT} \left( 16,256\,k+42 \right) =[[16,256\,k+42],[3+16\,k,-1-6 \,k]] {\it PISOT} \left( 16,256\,k+44 \right) =[[16,256\,k+44,4096\,{k}^{2}+ 1408\,k+121,65536\,{k}^{3}+33792\,{k}^{2}+5808\,k+333,1048576\,{k}^{4}+ 720896\,{k}^{3}+185856\,{k}^{2}+21304\,k+916],[3+16\,k,-1-4\,k,1+5\,k,- 2\,k,-1-6\,k]] {\it PISOT} \left( 16,256\,k+51 \right) =[[16,256\,k+51,4096\,{k}^{2}+ 1632\,k+163],[3+16\,k,3\,k,2+10\,k]] {\it PISOT} \left( 16,256\,k+56 \right) =[[16,256\,k+56,4096\,{k}^{2}+ 1792\,k+196,65536\,{k}^{3}+43008\,{k}^{2}+9408\,k+686,1048576\,{k}^{4}+ 917504\,{k}^{3}+301056\,{k}^{2}+43904\,k+2401],[4+16\,k,-2-8\,k,1+4\,k, -1-2\,k,2+9\,k]] {\it PISOT} \left( 16,256\,k+57 \right) =[[16,256\,k+57],[3+16\,k,2+9\, k]] {\it PISOT} \left( 16,256\,k+58 \right) =[[16,256\,k+58,4096\,{k}^{2}+ 1856\,k+210,65536\,{k}^{3}+44544\,{k}^{2}+10084\,k+760,1048576\,{k}^{4} +950272\,{k}^{3}+322752\,{k}^{2}+48680\,k+2750,16777216\,{k}^{5}+ 19005440\,{k}^{4}+8607744\,{k}^{3}+1948072\,{k}^{2}+220260\,k+9951],[4+ 16\,k,-2-6\,k,2+10\,k,1+4\,k,-1-2\,k,2+9\,k]] {\it PISOT} \left( 16,256\,k+62 \right) =[[16,256\,k+62,4096\,{k}^{2}+ 1984\,k+240,65536\,{k}^{3}+47616\,{k}^{2}+11524\,k+929,1048576\,{k}^{4} +1015808\,{k}^{3}+368832\,{k}^{2}+59488\,k+3596],[4+16\,k,-2\,k,-2-8\,k ,k,1+4\,k]] {\it PISOT} \left( 16,256\,k+63 \right) =[[16,256\,k+63,4096\,{k}^{2}+ 2016\,k+248],[4+16\,k,-k,-1-4\,k]] {\it PISOT} \left( 16,256\,k+65 \right) =[[16,256\,k+65,4096\,{k}^{2}+ 2080\,k+264],[4+16\,k,k,1+4\,k]] {\it PISOT} \left( 16,256\,k+66 \right) =[[16,256\,k+66,4096\,{k}^{2}+ 2112\,k+272,65536\,{k}^{3}+50688\,{k}^{2}+13060\,k+1121,1048576\,{k}^{4 }+1081344\,{k}^{3}+417984\,{k}^{2}+71776\,k+4620],[4+16\,k,2\,k,2+8\,k, k,1+4\,k]] {\it PISOT} \left( 16,256\,k+69 \right) =[[16,256\,k+69,4096\,{k}^{2}+ 2208\,k+298],[3+16\,k,5+21\,k,3+11\,k]] {\it PISOT} \left( 16,256\,k+70 \right) =[[16,256\,k+70,4096\,{k}^{2}+ 2240\,k+306,65536\,{k}^{3}+53760\,{k}^{2}+14692\,k+1338,1048576\,{k}^{4 }+1146880\,{k}^{3}+470208\,{k}^{2}+85656\,k+5850,16777216\,{k}^{5}+ 22937600\,{k}^{4}+12539904\,{k}^{3}+3426904\,{k}^{2}+468156\,k+25577],[ 4+16\,k,2+6\,k,-2-6\,k,2+6\,k,-1-6\,k,-3-11\,k]] {\it PISOT} \left( 16,256\,k+72 \right) =[[16,256\,k+72,4096\,{k}^{2}+ 2304\,k+324,65536\,{k}^{3}+55296\,{k}^{2}+15552\,k+1458,1048576\,{k}^{4 }+1179648\,{k}^{3}+497664\,{k}^{2}+93312\,k+6561],[5+16\,k,-2-8\,k,-1-4 \,k,-1-2\,k,2+7\,k]] {\it PISOT} \left( 16,256\,k+73 \right) =[[16,256\,k+73],[5+16\,k,-2-7 \,k]] {\it PISOT} \left( 16,256\,k+74 \right) =[[16,256\,k+74,4096\,{k}^{2}+ 2368\,k+342,65536\,{k}^{3}+56832\,{k}^{2}+16420\,k+1581,1048576\,{k}^{4 }+1212416\,{k}^{3}+525504\,{k}^{2}+101208\,k+7309,16777216\,{k}^{5}+ 24248320\,{k}^{4}+14014464\,{k}^{3}+4049000\,{k}^{2}+584840\,k+33790],[ 5+16\,k,-2-6\,k,1+4\,k,1+3\,k,-1-2\,k,2+7\,k]] {\it PISOT} \left( 16,256\,k+77 \right) =[[16,256\,k+77,4096\,{k}^{2}+ 2464\,k+371,65536\,{k}^{3}+59136\,{k}^{2}+17801\,k+1788],[5+16\,k,-1-3 \,k,2\,k,3+10\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998476198215330 {\it PISOT} \left( 16,256\,k+82 \right) =[[16,256\,k+82,4096\,{k}^{2}+ 2624\,k+420,65536\,{k}^{3}+62976\,{k}^{2}+20164\,k+2151],[4+16\,k,5+18 \,k,4+12\,k,-1-3\,k]] {\it PISOT} \left( 16,256\,k+83 \right) =[[16,256\,k+83],[5+16\,k,1+3\, k]] {\it PISOT} \left( 16,256\,k+84 \right) =[[16,256\,k+84,4096\,{k}^{2}+ 2688\,k+441,65536\,{k}^{3}+64512\,{k}^{2}+21168\,k+2315],[5+16\,k,1+4\, k,2+5\,k,-2-6\,k]] {\it PISOT} \left( 16,256\,k+85 \right) =[[16,256\,k+85,4096\,{k}^{2}+ 2720\,k+452],[6+16\,k,-4-11\,k,2+6\,k]] {\it PISOT} \left( 16,256\,k+86 \right) =[[16,256\,k+86],[5+16\,k,2+6\, k]] {\it PISOT} \left( 16,256\,k+87 \right) =[[16,256\,k+87,4096\,{k}^{2}+ 2784\,k+473,65536\,{k}^{3}+66816\,{k}^{2}+22705\,k+2572],[5+16\,k,3+7\, k,-3-10\,k,-2-6\,k]] {\it PISOT} \left( 16,256\,k+95 \right) =[[16,256\,k+95,4096\,{k}^{2}+ 3040\,k+564,65536\,{k}^{3}+72960\,{k}^{2}+27073\,k+3348,1048576\,{k}^{4 }+1556480\,{k}^{3}+866352\,{k}^{2}+214296\,k+19874],[6+16\,k,-k,-2-6\,k ,-2-4\,k,3+8\,k]] {\it PISOT} \left( 16,256\,k+97 \right) =[[16,256\,k+97,4096\,{k}^{2}+ 3104\,k+588,65536\,{k}^{3}+74496\,{k}^{2}+28225\,k+3564,1048576\,{k}^{4 }+1589248\,{k}^{3}+903216\,{k}^{2}+228120\,k+21602],[6+16\,k,k,2+6\,k,1 +4\,k,3+8\,k]] {\it PISOT} \left( 16,256\,k+99 \right) =[[16,256\,k+99],[7+16\,k,-5-13 \,k]] {\it PISOT} \left( 16,256\,k+101 \right) =[[16,256\,k+101],[6+16\,k,2+5 \,k]] {\it PISOT} \left( 16,256\,k+102 \right) =[[16,256\,k+102],[7+16\,k,-4- 10\,k]] {\it PISOT} \left( 16,256\,k+110 \right) =[[16,256\,k+110],[6+16\,k,6+ 14\,k]] {\it PISOT} \left( 16,256\,k+111 \right) =[[16,256\,k+111,4096\,{k}^{2} +3552\,k+770,65536\,{k}^{3}+85248\,{k}^{2}+36961\,k+5341],[6+16\,k,6+15 \,k,3+8\,k,3+7\,k]] {\it PISOT} \left( 16,256\,k+113 \right) =[[16,256\,k+113,4096\,{k}^{2} +3616\,k+798],[7+16\,k,1+k,-4-9\,k]] {\it PISOT} \left( 16,256\,k+117 \right) =[[16,256\,k+117],[8+16\,k,-5- 11\,k]] {\it PISOT} \left( 16,256\,k+124 \right) =[[16,256\,k+124,4096\,{k}^{2} +3968\,k+961,65536\,{k}^{3}+95232\,{k}^{2}+46128\,k+7448,1048576\,{k}^{ 4}+2031616\,{k}^{3}+1476096\,{k}^{2}+476664\,k+57724],[8+16\,k,-2-4\,k, 1+k,-4-8\,k,1+2\,k]] {\it PISOT} \left( 16,256\,k+126 \right) =[[16,256\,k+126],[8+16\,k,-1- 2\,k]] {\it PISOT} \left( 16,256\,k+127 \right) =[[16,256\,k+127,4096\,{k}^{2} +4064\,k+1008],[8+16\,k,-1-k,4+8\,k]] {\it PISOT} \left( 16,256\,k+129 \right) =[[16,256\,k+129,4096\,{k}^{2} +4128\,k+1040],[8+16\,k,k,4+8\,k]] {\it PISOT} \left( 16,256\,k+130 \right) =[[16,256\,k+130],[8+16\,k,1+2 \,k]] {\it PISOT} \left( 16,256\,k+132 \right) =[[16,256\,k+132,4096\,{k}^{2} +4224\,k+1089,65536\,{k}^{3}+101376\,{k}^{2}+52272\,k+8984,1048576\,{k} ^{4}+2162688\,{k}^{3}+1672704\,{k}^{2}+574984\,k+74116],[8+16\,k,2+4\,k ,1+k,-4-8\,k,-1-2\,k]] {\it PISOT} \left( 16,256\,k+139 \right) =[[16,256\,k+139],[8+16\,k,6+ 11\,k]] {\it PISOT} \left( 16,256\,k+143 \right) =[[16,256\,k+143,4096\,{k}^{2} +4576\,k+1278],[9+16\,k,-k,-5-9\,k]] {\it PISOT} \left( 16,256\,k+145 \right) =[[16,256\,k+145,4096\,{k}^{2} +4640\,k+1314,65536\,{k}^{3}+111360\,{k}^{2}+63073\,k+11908],[10+16\,k, -9-15\,k,5+8\,k,-4-7\,k]] {\it PISOT} \left( 16,256\,k+146 \right) =[[16,256\,k+146],[10+16\,k,-8 -14\,k]] {\it PISOT} \left( 16,256\,k+154 \right) =[[16,256\,k+154],[9+16\,k,6+ 10\,k]] {\it PISOT} \left( 16,256\,k+155 \right) =[[16,256\,k+155],[10+16\,k,-3 -5\,k]] {\it PISOT} \left( 16,256\,k+157 \right) =[[16,256\,k+157],[9+16\,k,8+ 13\,k]] {\it PISOT} \left( 16,256\,k+159 \right) =[[16,256\,k+159,4096\,{k}^{2} +5088\,k+1580,65536\,{k}^{3}+122112\,{k}^{2}+75841\,k+15701,1048576\,{k }^{4}+2605056\,{k}^{3}+2426928\,{k}^{2}+1004872\,k+156026],[10+16\,k,-1 -k,4+6\,k,-3-4\,k,5+8\,k]] {\it PISOT} \left( 16,256\,k+161 \right) =[[16,256\,k+161,4096\,{k}^{2} +5152\,k+1620,65536\,{k}^{3}+123648\,{k}^{2}+77761\,k+16301,1048576\,{k }^{4}+2637824\,{k}^{3}+2488368\,{k}^{2}+1043272\,k+164026],[10+16\,k,1+ k,-4-6\,k,2+4\,k,5+8\,k]] {\it PISOT} \left( 16,256\,k+169 \right) =[[16,256\,k+169,4096\,{k}^{2} +5408\,k+1785,65536\,{k}^{3}+129792\,{k}^{2}+85681\,k+18853],[11+16\,k, -4-7\,k,-7-10\,k,4+6\,k]] {\it PISOT} \left( 16,256\,k+170 \right) =[[16,256\,k+170],[11+16\,k,-4 -6\,k]] {\it PISOT} \left( 16,256\,k+171 \right) =[[16,256\,k+171,4096\,{k}^{2} +5472\,k+1828],[10+16\,k,7+11\,k,4+6\,k]] {\it PISOT} \left( 16,256\,k+172 \right) =[[16,256\,k+172,4096\,{k}^{2} +5504\,k+1849,65536\,{k}^{3}+132096\,{k}^{2}+88752\,k+19877],[11+16\,k, -3-4\,k,3+5\,k,4+6\,k]] {\it PISOT} \left( 16,256\,k+173 \right) =[[16,256\,k+173],[11+16\,k,-2 -3\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998474997380933 {\it PISOT} \left( 16,256\,k+174 \right) =[[16,256\,k+174,4096\,{k}^{2} +5568\,k+1892,65536\,{k}^{3}+133632\,{k}^{2}+90820\,k+20573],[12+16\,k, -13-18\,k,8+12\,k,2+3\,k]] {\it PISOT} \left( 16,256\,k+179 \right) =[[16,256\,k+179,4096\,{k}^{2} +5728\,k+2003,65536\,{k}^{3}+137472\,{k}^{2}+96137\,k+22413],[11+16\,k, 2+3\,k,2+2\,k,-7-10\,k]] {\it PISOT} \left( 16,256\,k+182 \right) =[[16,256\,k+182,4096\,{k}^{2} +5824\,k+2070,65536\,{k}^{3}+139776\,{k}^{2}+99364\,k+23543,1048576\,{k }^{4}+2981888\,{k}^{3}+3179712\,{k}^{2}+1506856\,k+267765,16777216\,{k} ^{5}+59637760\,{k}^{4}+84793344\,{k}^{3}+60276632\,{k}^{2}+21423032\,k+ 3045410],[11+16\,k,4+6\,k,3+4\,k,-2-3\,k,-1-2\,k,-5-7\,k]] {\it PISOT} \left( 16,256\,k+183 \right) =[[16,256\,k+183],[11+16\,k,5+ 7\,k]] {\it PISOT} \left( 16,256\,k+184 \right) =[[16,256\,k+184,4096\,{k}^{2} +5888\,k+2116,65536\,{k}^{3}+141312\,{k}^{2}+101568\,k+24334,1048576\,{ k}^{4}+3014656\,{k}^{3}+3250176\,{k}^{2}+1557376\,k+279841],[12+16\,k,- 6-8\,k,3+4\,k,-1-2\,k,-5-7\,k]] {\it PISOT} \left( 16,256\,k+186 \right) =[[16,256\,k+186,4096\,{k}^{2} +5952\,k+2162,65536\,{k}^{3}+142848\,{k}^{2}+103780\,k+25130,1048576\,{ k}^{4}+3047424\,{k}^{3}+3321024\,{k}^{2}+1608424\,k+292098,16777216\,{k }^{5}+60948480\,{k}^{4}+88561664\,{k}^{3}+64339368\,{k}^{2}+23369740\,k +3395195],[12+16\,k,-4-6\,k,-4-6\,k,-4-6\,k,-5-6\,k,8+11\,k]] {\it PISOT} \left( 16,256\,k+187 \right) =[[16,256\,k+187,4096\,{k}^{2} +5984\,k+2186],[13+16\,k,-16-21\,k,8+11\,k]] {\it PISOT} \left( 16,256\,k+190 \right) =[[16,256\,k+190,4096\,{k}^{2} +6080\,k+2256,65536\,{k}^{3}+145920\,{k}^{2}+108292\,k+26787,1048576\,{ k}^{4}+3112960\,{k}^{3}+3465408\,{k}^{2}+1714464\,k+318060],[12+16\,k,- 2-2\,k,6+8\,k,-1-k,3+4\,k]] {\it PISOT} \left( 16,256\,k+191 \right) =[[16,256\,k+191,4096\,{k}^{2} +6112\,k+2280],[12+16\,k,-1-k,3+4\,k]] {\it PISOT} \left( 16,256\,k+193 \right) =[[16,256\,k+193,4096\,{k}^{2} +6176\,k+2328],[12+16\,k,1+k,-3-4\,k]] {\it PISOT} \left( 16,256\,k+194 \right) =[[16,256\,k+194,4096\,{k}^{2} +6208\,k+2352,65536\,{k}^{3}+148992\,{k}^{2}+112900\,k+28515,1048576\,{ k}^{4}+3178496\,{k}^{3}+3612864\,{k}^{2}+1825056\,k+345708],[12+16\,k,2 +2\,k,-6-8\,k,-1-k,3+4\,k]] {\it PISOT} \left( 16,256\,k+198 \right) =[[16,256\,k+198,4096\,{k}^{2} +6336\,k+2450,65536\,{k}^{3}+152064\,{k}^{2}+117604\,k+30316,1048576\,{ k}^{4}+3244032\,{k}^{3}+3763392\,{k}^{2}+1940312\,k+375126,16777216\,{k }^{5}+64880640\,{k}^{4}+100358144\,{k}^{3}+77614680\,{k}^{2}+30011668\, k+4641757],[12+16\,k,4+6\,k,8+10\,k,-3-4\,k,-1-2\,k,-7-9\,k]] {\it PISOT} \left( 16,256\,k+199 \right) =[[16,256\,k+199],[13+16\,k,-7 -9\,k]] {\it PISOT} \left( 16,256\,k+205 \right) =[[16,256\,k+205,4096\,{k}^{2} +6560\,k+2627],[13+16\,k,-3-3\,k,8+10\,k]] {\it PISOT} \left( 16,256\,k+212 \right) =[[16,256\,k+212,4096\,{k}^{2} +6784\,k+2809,65536\,{k}^{3}+162816\,{k}^{2}+134832\,k+37219,1048576\,{ k}^{4}+3473408\,{k}^{3}+4314624\,{k}^{2}+2382024\,k+493148],[13+16\,k,3 +4\,k,4+5\,k,2+2\,k,-5-6\,k]] {\it PISOT} \left( 16,256\,k+214 \right) =[[16,256\,k+214],[13+16\,k,5+ 6\,k]] {\it PISOT} \left( 16,256\,k+219 \right) =[[16,256\,k+219,4096\,{k}^{2} +7008\,k+2998],[13+16\,k,9+11\,k,6+7\,k]] {\it PISOT} \left( 16,256\,k+220 \right) =[[16,256\,k+220,4096\,{k}^{2} +7040\,k+3025],[14+16\,k,-3-4\,k,-6-7\,k]] {\it PISOT} \left( 16,256\,k+221 \right) =[[16,256\,k+221,4096\,{k}^{2} +7072\,k+3053,65536\,{k}^{3}+169728\,{k}^{2}+146537\,k+42176,1048576\,{ k}^{4}+3620864\,{k}^{3}+4689072\,{k}^{2}+2699058\,k+582645,16777216\,{k }^{5}+72417280\,{k}^{4}+125040128\,{k}^{3}+107957477\,{k}^{2}+46607241 \,k+8049014],[15+16\,k,-17-19\,k,9+10\,k,-5-6\,k,-3-3\,k,6+7\,k]] {\it PISOT} \left( 16,256\,k+223 \right) =[[16,256\,k+223,4096\,{k}^{2} +7136\,k+3108,65536\,{k}^{3}+171264\,{k}^{2}+149185\,k+43317,1048576\,{ k}^{4}+3653632\,{k}^{3}+4773936\,{k}^{2}+2772312\,k+603720],[14+16\,k,- 1-k,2+2\,k,-4-4\,k,7+8\,k]] {\it PISOT} \left( 16,256\,k+225 \right) =[[16,256\,k+225,4096\,{k}^{2} +7200\,k+3164,65536\,{k}^{3}+172800\,{k}^{2}+151873\,k+44493,1048576\,{ k}^{4}+3686400\,{k}^{3}+4859952\,{k}^{2}+2847576\,k+625672],[14+16\,k,1 +k,-2-2\,k,3+4\,k,7+8\,k]] {\it PISOT} \left( 16,256\,k+228 \right) =[[16,256\,k+228,4096\,{k}^{2} +7296\,k+3249],[14+16\,k,3+4\,k,8+9\,k]] {\it PISOT} \left( 16,256\,k+230 \right) =[[16,256\,k+230],[15+16\,k,-9 -10\,k]] {\it PISOT} \left( 16,256\,k+231 \right) =[[16,256\,k+231,4096\,{k}^{2} +7392\,k+3335,65536\,{k}^{3}+177408\,{k}^{2}+160081\,k+48148,1048576\,{ k}^{4}+3784704\,{k}^{3}+5122608\,{k}^{2}+3081506\,k+695121,16777216\,{k }^{5}+75694080\,{k}^{4}+136603136\,{k}^{3}+123261015\,{k}^{2}+55610473 \,k+10035582],[14+16\,k,6+7\,k,5+5\,k,-7-8\,k,-3-4\,k,-9-10\,k]] {\it PISOT} \left( 16,256\,k+235 \right) =[[16,256\,k+235,4096\,{k}^{2} +7520\,k+3452],[16+16\,k,-20-21\,k,11+12\,k]] {\it PISOT} \left( 16,256\,k+238 \right) =[[16,256\,k+238],[14+16\,k,13 +14\,k]] {\it PISOT} \left( 16,256\,k+239 \right) =[[16,256\,k+239],[14+16\,k,14 +15\,k]] {\it PISOT} \left( 16,256\,k+247 \right) =[[16,256\,k+247,4096\,{k}^{2} +7904\,k+3813,65536\,{k}^{3}+189696\,{k}^{2}+183025\,k+58862,1048576\,{ k}^{4}+4046848\,{k}^{3}+5856816\,{k}^{2}+3767206\,k+908664,16777216\,{k }^{5}+80936960\,{k}^{4}+156182016\,{k}^{3}+150689095\,{k}^{2}+72694045 \,k+14027221],[16+16\,k,-9-9\,k,5+5\,k,-3-3\,k,2+2\,k,-1-k]] {\it PISOT} \left( 16,256\,k+248 \right) =[[16,256\,k+248,4096\,{k}^{2} +7936\,k+3844,65536\,{k}^{3}+190464\,{k}^{2}+184512\,k+59582,1048576\,{ k}^{4}+4063232\,{k}^{3}+5904384\,{k}^{2}+3813248\,k+923521],[16+16\,k,- 8-8\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 16,256\,k+249 \right) =[[16,256\,k+249,4096\,{k}^{2} +7968\,k+3875,65536\,{k}^{3}+191232\,{k}^{2}+186001\,k+60304],[16+16\,k ,-7-7\,k,3+3\,k,-1-k]] {\it PISOT} \left( 16,256\,k+250 \right) =[[16,256\,k+250,4096\,{k}^{2} +8000\,k+3906,65536\,{k}^{3}+192000\,{k}^{2}+187492\,k+61027],[16+16\,k ,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 16,256\,k+251 \right) =[[16,256\,k+251,4096\,{k}^{2} +8032\,k+3938,65536\,{k}^{3}+192768\,{k}^{2}+189017\,k+61784],[16+16\,k ,-5-5\,k,2+2\,k,-1-k]] {\it PISOT} \left( 16,256\,k+252 \right) =[[16,256\,k+252,4096\,{k}^{2} +8064\,k+3969],[16+16\,k,-4-4\,k,1+k]] {\it PISOT} \left( 16,256\,k+253 \right) =[[16,256\,k+253,4096\,{k}^{2} +8096\,k+4001],[16+16\,k,-3-3\,k,1+k]] {\it PISOT} \left( 16,256\,k+254 \right) =[[16,256\,k+254],[16+16\,k,-2 -2\,k]] {\it PISOT} \left( 16,256\,k+255 \right) =[[16,256\,k+255],[16+16\,k,-1 -k]] {\it PISOT} \left( 17,289\,k+1 \right) =[[17,289\,k+1],[17\,k,k]] {\it PISOT} \left( 17,289\,k+2 \right) =[[17,289\,k+2],[17\,k,2\,k]] {\it PISOT} \left( 17,289\,k+3 \right) =[[17,289\,k+3,4913\,{k}^{2}+102 \,k+1],[17\,k,3\,k,k]] {\it PISOT} \left( 17,289\,k+4 \right) =[[17,289\,k+4,4913\,{k}^{2}+136 \,k+1],[17\,k,4\,k,k]] {\it PISOT} \left( 17,289\,k+5 \right) =[[17,289\,k+5,4913\,{k}^{2}+170 \,k+1],[17\,k,5\,k,k]] {\it PISOT} \left( 17,289\,k+6 \right) =[[17,289\,k+6,4913\,{k}^{2}+204 \,k+2,83521\,{k}^{3}+5202\,{k}^{2}+104\,k+1],[17\,k,6\,k,2\,k,k]] {\it PISOT} \left( 17,289\,k+7 \right) =[[17,289\,k+7,4913\,{k}^{2}+238 \,k+3,83521\,{k}^{3}+6069\,{k}^{2}+151\,k+1],[17\,k,7\,k,3\,k,k]] {\it PISOT} \left( 17,289\,k+8 \right) =[[17,289\,k+8,4913\,{k}^{2}+272 \,k+4,83521\,{k}^{3}+6936\,{k}^{2}+200\,k+2,1419857\,{k}^{4}+157216\,{k }^{3}+6732\,{k}^{2}+132\,k+1],[17\,k,8\,k,4\,k,2\,k,k]] {\it PISOT} \left( 17,289\,k+9 \right) =[[17,289\,k+9,4913\,{k}^{2}+306 \,k+5,83521\,{k}^{3}+7803\,{k}^{2}+251\,k+3,1419857\,{k}^{4}+176868\,{k }^{3}+8466\,{k}^{2}+192\,k+2,24137569\,{k}^{5}+3758445\,{k}^{4}+238714 \,{k}^{3}+7920\,{k}^{2}+147\,k+1],[1+17\,k,-8\,k,-4\,k,-2\,k,-k,-k]] {\it PISOT} \left( 17,289\,k+11 \right) =[[17,289\,k+11,4913\,{k}^{2}+ 374\,k+7,83521\,{k}^{3}+9537\,{k}^{2}+359\,k+4,1419857\,{k}^{4}+216172 \,{k}^{3}+12240\,{k}^{2}+290\,k+2,24137569\,{k}^{5}+4593655\,{k}^{4}+ 347378\,{k}^{3}+12653\,{k}^{2}+205\,k+1],[17\,k,11\,k,7\,k,4\,k,2\,k,k] ] {\it PISOT} \left( 17,289\,k+18 \right) =[[17,289\,k+18],[2+17\,k,-1-16 \,k]] {\it PISOT} \left( 17,289\,k+19 \right) =[[17,289\,k+19],[2+17\,k,-1-15 \,k]] {\it PISOT} \left( 17,289\,k+30 \right) =[[17,289\,k+30,4913\,{k}^{2}+ 1020\,k+53,83521\,{k}^{3}+26010\,{k}^{2}+2702\,k+94,1419857\,{k}^{4}+ 589560\,{k}^{3}+91851\,{k}^{2}+6376\,k+167],[1+17\,k,1+13\,k,1+6\,k,-6 \,k,-1-10\,k]] {\it PISOT} \left( 17,289\,k+31 \right) =[[17,289\,k+31,4913\,{k}^{2}+ 1054\,k+57],[1+17\,k,1+14\,k,1+9\,k]] {\it PISOT} \left( 17,289\,k+32 \right) =[[17,289\,k+32,4913\,{k}^{2}+ 1088\,k+60,83521\,{k}^{3}+27744\,{k}^{2}+3064\,k+112],[2+17\,k,-2\,k,-1 -4\,k,1+9\,k]] {\it PISOT} \left( 17,289\,k+36 \right) =[[17,289\,k+36,4913\,{k}^{2}+ 1224\,k+76,83521\,{k}^{3}+31212\,{k}^{2}+3880\,k+160],[2+17\,k,2\,k,4\, k,1+8\,k]] {\it PISOT} \left( 17,289\,k+40 \right) =[[17,289\,k+40,4913\,{k}^{2}+ 1360\,k+94,83521\,{k}^{3}+34680\,{k}^{2}+4796\,k+221,1419857\,{k}^{4}+ 786080\,{k}^{3}+163098\,{k}^{2}+15034\,k+520],[2+17\,k,1+6\,k,-1-3\,k,1 +10\,k,1+7\,k]] {\it PISOT} \left( 17,289\,k+41 \right) =[[17,289\,k+41],[2+17\,k,1+7\, k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.979540393002514 {\it PISOT} \left( 17,289\,k+44 \right) =[[17,289\,k+44,4913\,{k}^{2}+ 1496\,k+114,83521\,{k}^{3}+38148\,{k}^{2}+5812\,k+295,1419857\,{k}^{4}+ 864688\,{k}^{3}+197574\,{k}^{2}+20062\,k+763,24137569\,{k}^{5}+18374620 \,{k}^{4}+5597352\,{k}^{3}+852581\,{k}^{2}+64898\,k+1973],[3+17\,k,-1-7 \,k,-k,-3\,k,-2-8\,k,2+13\,k]] {\it PISOT} \left( 17,289\,k+45 \right) =[[17,289\,k+45,4913\,{k}^{2}+ 1530\,k+119,83521\,{k}^{3}+39015\,{k}^{2}+6071\,k+315],[2+17\,k,2+11\,k ,-5\,k,-2-13\,k]] {\it PISOT} \left( 17,289\,k+47 \right) =[[17,289\,k+47,4913\,{k}^{2}+ 1598\,k+130],[3+17\,k,-1-4\,k,1+6\,k]] {\it PISOT} \left( 17,289\,k+48 \right) =[[17,289\,k+48,4913\,{k}^{2}+ 1632\,k+136],[2+17\,k,2+14\,k,1+6\,k]] {\it PISOT} \left( 17,289\,k+49 \right) =[[17,289\,k+49,4913\,{k}^{2}+ 1666\,k+141],[3+17\,k,-2\,k,-1-6\,k]] {\it PISOT} \left( 17,289\,k+53 \right) =[[17,289\,k+53,4913\,{k}^{2}+ 1802\,k+165],[3+17\,k,1+2\,k,-2-11\,k]] {\it PISOT} \left( 17,289\,k+57 \right) =[[17,289\,k+57,4913\,{k}^{2}+ 1938\,k+191,83521\,{k}^{3}+49419\,{k}^{2}+9743\,k+640],[3+17\,k,1+6\,k, 3\,k,2+10\,k]] {\it PISOT} \left( 17,289\,k+58 \right) =[[17,289\,k+58],[4+17\,k,-2-10 \,k]] {\it PISOT} \left( 17,289\,k+64 \right) =[[17,289\,k+64,4913\,{k}^{2}+ 2176\,k+241,83521\,{k}^{3}+55488\,{k}^{2}+12290\,k+908],[4+17\,k,-1-4\, k,1+2\,k,-2-9\,k]] {\it PISOT} \left( 17,289\,k+65 \right) =[[17,289\,k+65,4913\,{k}^{2}+ 2210\,k+249],[5+17\,k,-5-20\,k,2+9\,k]] {\it PISOT} \left( 17,289\,k+67 \right) =[[17,289\,k+67,4913\,{k}^{2}+ 2278\,k+264],[4+17\,k,-1-k,3+13\,k]] {\it PISOT} \left( 17,289\,k+71 \right) =[[17,289\,k+71,4913\,{k}^{2}+ 2414\,k+297],[4+17\,k,1+3\,k,-1-4\,k]] {\it PISOT} \left( 17,289\,k+72 \right) =[[17,289\,k+72],[4+17\,k,1+4\, k]] {\it PISOT} \left( 17,289\,k+73 \right) =[[17,289\,k+73,4913\,{k}^{2}+ 2482\,k+313],[4+17\,k,1+5\,k,1+4\,k]] {\it PISOT} \left( 17,289\,k+74 \right) =[[17,289\,k+74,4913\,{k}^{2}+ 2516\,k+322,83521\,{k}^{3}+64158\,{k}^{2}+16424\,k+1401],[5+17\,k,-3-11 \,k,1+3\,k,-1-4\,k]] {\it PISOT} \left( 17,289\,k+75 \right) =[[17,289\,k+75,4913\,{k}^{2}+ 2550\,k+331,83521\,{k}^{3}+65025\,{k}^{2}+16879\,k+1461,1419857\,{k}^{4 }+1473900\,{k}^{3}+573852\,{k}^{2}+99324\,k+6449,24137569\,{k}^{5}+ 31320375\,{k}^{4}+16258562\,{k}^{3}+4220712\,{k}^{2}+547977\,k+28467],[ 5+17\,k,-2-10\,k,-3-10\,k,2+7\,k,-1-3\,k,1+4\,k]] {\it PISOT} \left( 17,289\,k+77 \right) =[[17,289\,k+77,4913\,{k}^{2}+ 2618\,k+349],[5+17\,k,-3-8\,k,4+15\,k]] {\it PISOT} \left( 17,289\,k+79 \right) =[[17,289\,k+79],[4+17\,k,3+11 \,k]] {\it PISOT} \left( 17,289\,k+82 \right) =[[17,289\,k+82],[4+17\,k,4+14 \,k]] {\it PISOT} \left( 17,289\,k+83 \right) =[[17,289\,k+83,4913\,{k}^{2}+ 2822\,k+405],[5+17\,k,-1-2\,k,2+7\,k]] {\it PISOT} \left( 17,289\,k+87 \right) =[[17,289\,k+87,4913\,{k}^{2}+ 2958\,k+445],[5+17\,k,2\,k,3+10\,k]] {\it PISOT} \left( 17,289\,k+89 \right) =[[17,289\,k+89],[6+17\,k,-4-13 \,k]] {\it PISOT} \left( 17,289\,k+95 \right) =[[17,289\,k+95,4913\,{k}^{2}+ 3230\,k+531,83521\,{k}^{3}+82365\,{k}^{2}+27079\,k+2968],[5+17\,k,3+10 \,k,2+5\,k,-2-6\,k]] {\it PISOT} \left( 17,289\,k+96 \right) =[[17,289\,k+96],[6+17\,k,-2-6 \,k]] {\it PISOT} \left( 17,289\,k+97 \right) =[[17,289\,k+97],[5+17\,k,4+12 \,k]] {\it PISOT} \left( 17,289\,k+98 \right) =[[17,289\,k+98,4913\,{k}^{2}+ 3332\,k+565,83521\,{k}^{3}+84966\,{k}^{2}+28814\,k+3257],[5+17\,k,4+13 \,k,2+7\,k,2+6\,k]] {\it PISOT} \left( 17,289\,k+99 \right) =[[17,289\,k+99],[6+17\,k,-1-3 \,k]] {\it PISOT} \left( 17,289\,k+100 \right) =[[17,289\,k+100,4913\,{k}^{2} +3400\,k+588],[5+17\,k,5+15\,k,1+3\,k]] {\it PISOT} \left( 17,289\,k+108 \right) =[[17,289\,k+108,4913\,{k}^{2} +3672\,k+686,83521\,{k}^{3}+93636\,{k}^{2}+34988\,k+4357],[6+17\,k,2+6 \,k,1+4\,k,3+8\,k]] {\it PISOT} \left( 17,289\,k+109 \right) =[[17,289\,k+109,4913\,{k}^{2} +3706\,k+699,83521\,{k}^{3}+94503\,{k}^{2}+35647\,k+4483,1419857\,{k}^{ 4}+2142068\,{k}^{3}+1211964\,{k}^{2}+304804\,k+28751],[6+17\,k,3+7\,k,- 2-6\,k,-2-4\,k,3+8\,k]] {\it PISOT} \left( 17,289\,k+114 \right) =[[17,289\,k+114],[7+17\,k,-2- 5\,k]] {\it PISOT} \left( 17,289\,k+115 \right) =[[17,289\,k+115,4913\,{k}^{2} +3910\,k+778],[7+17\,k,-1-4\,k,-4-10\,k]] {\it PISOT} \left( 17,289\,k+117 \right) =[[17,289\,k+117,4913\,{k}^{2} +3978\,k+805,83521\,{k}^{3}+101439\,{k}^{2}+41059\,k+5539],[6+17\,k,5+ 15\,k,7+18\,k,2+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.986496331876077 {\it PISOT} \left( 17,289\,k+123 \right) =[[17,289\,k+123,4913\,{k}^{2} +4182\,k+890,83521\,{k}^{3}+106641\,{k}^{2}+45389\,k+6440],[8+17\,k,-6- 13\,k,3+8\,k,3+7\,k]] {\it PISOT} \left( 17,289\,k+124 \right) =[[17,289\,k+124,4913\,{k}^{2} +4216\,k+904],[8+17\,k,-6-12\,k,6+14\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.976253041037944 {\it PISOT} \left( 17,289\,k+126 \right) =[[17,289\,k+126,4913\,{k}^{2} +4284\,k+934,83521\,{k}^{3}+109242\,{k}^{2}+47632\,k+6923,1419857\,{k}^ {4}+2476152\,{k}^{3}+1619454\,{k}^{2}+470750\,k+51315,24137569\,{k}^{5} +52618230\,{k}^{4}+45883952\,{k}^{3}+20006385\,{k}^{2}+4361662\,k+ 380360],[8+17\,k,-4-10\,k,-3-6\,k,3+6\,k,-3-6\,k,3+7\,k]] {\it PISOT} \left( 17,289\,k+128 \right) =[[17,289\,k+128],[7+17\,k,4+9 \,k]] {\it PISOT} \left( 17,289\,k+132 \right) =[[17,289\,k+132,4913\,{k}^{2} +4488\,k+1025,83521\,{k}^{3}+114444\,{k}^{2}+52274\,k+7959],[8+17\,k,-2 -4\,k,2+3\,k,-5-11\,k]] {\it PISOT} \left( 17,289\,k+139 \right) =[[17,289\,k+139,4913\,{k}^{2} +4726\,k+1137,83521\,{k}^{3}+120513\,{k}^{2}+57979\,k+9300,1419857\,{k} ^{4}+2731628\,{k}^{3}+1971150\,{k}^{2}+632286\,k+76069],[8+17\,k,2+3\,k ,-4-9\,k,-3-6\,k,1+2\,k]] {\it PISOT} \left( 17,289\,k+141 \right) =[[17,289\,k+141,4913\,{k}^{2} +4794\,k+1169],[9+17\,k,-6-12\,k,1+2\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998381804829322 {\it PISOT} \left( 17,289\,k+142 \right) =[[17,289\,k+142,4913\,{k}^{2} +4828\,k+1186,83521\,{k}^{3}+123114\,{k}^{2}+60488\,k+9906],[8+17\,k,2+ 6\,k,8+16\,k,-1-2\,k]] {\it PISOT} \left( 17,289\,k+143 \right) =[[17,289\,k+143,4913\,{k}^{2} +4862\,k+1203,83521\,{k}^{3}+123981\,{k}^{2}+61351\,k+10120],[9+17\,k,- 5-10\,k,k,4+8\,k]] {\it PISOT} \left( 17,289\,k+144 \right) =[[17,289\,k+144],[8+17\,k,4+8 \,k]] {\it PISOT} \left( 17,289\,k+145 \right) =[[17,289\,k+145],[9+17\,k,-4- 8\,k]] {\it PISOT} \left( 17,289\,k+146 \right) =[[17,289\,k+146,4913\,{k}^{2} +4964\,k+1254,83521\,{k}^{3}+126582\,{k}^{2}+63952\,k+10771],[8+17\,k,5 +10\,k,1+k,-4-8\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998380144090446 {\it PISOT} \left( 17,289\,k+147 \right) =[[17,289\,k+147,4913\,{k}^{2} +4998\,k+1271,83521\,{k}^{3}+127449\,{k}^{2}+64823\,k+10989],[9+17\,k,- 4-6\,k,8+16\,k,1+2\,k]] {\it PISOT} \left( 17,289\,k+148 \right) =[[17,289\,k+148,4913\,{k}^{2} +5032\,k+1288],[8+17\,k,6+12\,k,1+2\,k]] {\it PISOT} \left( 17,289\,k+150 \right) =[[17,289\,k+150,4913\,{k}^{2} +5100\,k+1324,83521\,{k}^{3}+130050\,{k}^{2}+67516\,k+11687,1419857\,{k }^{4}+2947800\,{k}^{3}+2295408\,{k}^{2}+794558\,k+103162],[9+17\,k,-1-3 \,k,-5-9\,k,3+6\,k,1+2\,k]] {\it PISOT} \left( 17,289\,k+157 \right) =[[17,289\,k+157,4913\,{k}^{2} +5338\,k+1450,83521\,{k}^{3}+136119\,{k}^{2}+73949\,k+13392],[9+17\,k,2 +4\,k,1+3\,k,6+11\,k]] {\it PISOT} \left( 17,289\,k+161 \right) =[[17,289\,k+161],[10+17\,k,-5 -9\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.976253392445487 {\it PISOT} \left( 17,289\,k+163 \right) =[[17,289\,k+163,4913\,{k}^{2} +5542\,k+1563,83521\,{k}^{3}+141321\,{k}^{2}+79711\,k+14988,1419857\,{k }^{4}+3203276\,{k}^{3}+2710140\,{k}^{2}+1019130\,k+143724,24137569\,{k} ^{5}+68069615\,{k}^{4}+76786722\,{k}^{3}+43311781\,{k}^{2}+12215673\,k+ 1378208],[9+17\,k,6+10\,k,-3-6\,k,-3-6\,k,-3-6\,k,-4-7\,k]] {\it PISOT} \left( 17,289\,k+165 \right) =[[17,289\,k+165,4913\,{k}^{2} +5610\,k+1601],[9+17\,k,6+12\,k,8+14\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.986494936069970 {\it PISOT} \left( 17,289\,k+166 \right) =[[17,289\,k+166,4913\,{k}^{2} +5644\,k+1621,83521\,{k}^{3}+143922\,{k}^{2}+82670\,k+15829],[9+17\,k,7 +13\,k,5+8\,k,-4-7\,k]] {\it PISOT} \left( 17,289\,k+172 \right) =[[17,289\,k+172,4913\,{k}^{2} +5848\,k+1740,83521\,{k}^{3}+149124\,{k}^{2}+88744\,k+17602],[11+17\,k, -10-15\,k,11+18\,k,-3-5\,k]] {\it PISOT} \left( 17,289\,k+174 \right) =[[17,289\,k+174,4913\,{k}^{2} +5916\,k+1781],[10+17\,k,3+4\,k,-6-10\,k]] {\it PISOT} \left( 17,289\,k+175 \right) =[[17,289\,k+175],[10+17\,k,3+ 5\,k]] {\it PISOT} \left( 17,289\,k+180 \right) =[[17,289\,k+180,4913\,{k}^{2} +6120\,k+1906,83521\,{k}^{3}+156060\,{k}^{2}+97204\,k+20182,1419857\,{k }^{4}+3537360\,{k}^{3}+3304902\,{k}^{2}+1372348\,k+213700],[11+17\,k,-4 -7\,k,-4-6\,k,2+4\,k,5+8\,k]] {\it PISOT} \left( 17,289\,k+181 \right) =[[17,289\,k+181,4913\,{k}^{2} +6154\,k+1927,83521\,{k}^{3}+156927\,{k}^{2}+98279\,k+20516],[11+17\,k, -4-6\,k,3+4\,k,-5-8\,k]] {\it PISOT} \left( 17,289\,k+189 \right) =[[17,289\,k+189,4913\,{k}^{2} +6426\,k+2101],[12+17\,k,-10-15\,k,2+3\,k]] {\it PISOT} \left( 17,289\,k+190 \right) =[[17,289\,k+190],[11+17\,k,2+ 3\,k]] {\it PISOT} \left( 17,289\,k+191 \right) =[[17,289\,k+191,4913\,{k}^{2} +6494\,k+2146,83521\,{k}^{3}+165597\,{k}^{2}+109445\,k+24112],[12+17\,k ,-9-13\,k,5+7\,k,-4-6\,k]] {\it PISOT} \left( 17,289\,k+192 \right) =[[17,289\,k+192],[12+17\,k,-8 -12\,k]] {\it PISOT} \left( 17,289\,k+193 \right) =[[17,289\,k+193],[11+17\,k,4+ 6\,k]] {\it PISOT} \left( 17,289\,k+194 \right) =[[17,289\,k+194,4913\,{k}^{2} +6596\,k+2214,83521\,{k}^{3}+168198\,{k}^{2}+112912\,k+25267],[12+17\,k ,-7-10\,k,3+5\,k,4+6\,k]] {\it PISOT} \left( 17,289\,k+200 \right) =[[17,289\,k+200],[11+17\,k,9+ 13\,k]] {\it PISOT} \left( 17,289\,k+202 \right) =[[17,289\,k+202,4913\,{k}^{2} +6868\,k+2400],[12+17\,k,-2-2\,k,7+10\,k]] {\it PISOT} \left( 17,289\,k+206 \right) =[[17,289\,k+206,4913\,{k}^{2} +7004\,k+2496],[12+17\,k,1+2\,k,5+7\,k]] {\it PISOT} \left( 17,289\,k+207 \right) =[[17,289\,k+207],[13+17\,k,- 10-14\,k]] {\it PISOT} \left( 17,289\,k+210 \right) =[[17,289\,k+210],[13+17\,k,-8 -11\,k]] {\it PISOT} \left( 17,289\,k+212 \right) =[[17,289\,k+212,4913\,{k}^{2} +7208\,k+2644],[12+17\,k,5+8\,k,11+15\,k]] {\it PISOT} \left( 17,289\,k+214 \right) =[[17,289\,k+214,4913\,{k}^{2} +7276\,k+2694,83521\,{k}^{3}+185538\,{k}^{2}+137392\,k+33914,1419857\,{ k}^{4}+4205528\,{k}^{3}+4671294\,{k}^{2}+2306108\,k+426934,24137569\,{k }^{5}+89367470\,{k}^{4}+132352752\,{k}^{3}+98008414\,{k}^{2}+36288584\, k+5374554],[12+17\,k,8+10\,k,-7-10\,k,-5-7\,k,-2-3\,k,-3-4\,k]] {\it PISOT} \left( 17,289\,k+215 \right) =[[17,289\,k+215,4913\,{k}^{2} +7310\,k+2719,83521\,{k}^{3}+186405\,{k}^{2}+138671\,k+34386],[12+17\,k ,8+11\,k,2+3\,k,3+4\,k]] {\it PISOT} \left( 17,289\,k+216 \right) =[[17,289\,k+216,4913\,{k}^{2} +7344\,k+2744],[13+17\,k,-4-5\,k,3+4\,k]] {\it PISOT} \left( 17,289\,k+217 \right) =[[17,289\,k+217],[13+17\,k,-3 -4\,k]] {\it PISOT} \left( 17,289\,k+218 \right) =[[17,289\,k+218,4913\,{k}^{2} +7412\,k+2796],[13+17\,k,-2-3\,k,-3-4\,k]] {\it PISOT} \left( 17,289\,k+222 \right) =[[17,289\,k+222,4913\,{k}^{2} +7548\,k+2899],[13+17\,k,k,10+13\,k]] {\it PISOT} \left( 17,289\,k+224 \right) =[[17,289\,k+224,4913\,{k}^{2} +7616\,k+2952],[12+17\,k,15+20\,k,7+9\,k]] {\it PISOT} \left( 17,289\,k+225 \right) =[[17,289\,k+225,4913\,{k}^{2} +7650\,k+2978,83521\,{k}^{3}+195075\,{k}^{2}+151877\,k+39415],[13+17\,k ,3+4\,k,1+2\,k,7+9\,k]] {\it PISOT} \left( 17,289\,k+231 \right) =[[17,289\,k+231],[13+17\,k,8+ 10\,k]] {\it PISOT} \left( 17,289\,k+232 \right) =[[17,289\,k+232,4913\,{k}^{2} +7888\,k+3166,83521\,{k}^{3}+201144\,{k}^{2}+161468\,k+43205],[14+17\,k ,-5-6\,k,3+3\,k,-8-10\,k]] {\it PISOT} \left( 17,289\,k+236 \right) =[[17,289\,k+236,4913\,{k}^{2} +8024\,k+3276],[14+17\,k,-1-2\,k,-9-11\,k]] {\it PISOT} \left( 17,289\,k+240 \right) =[[17,289\,k+240,4913\,{k}^{2} +8160\,k+3388],[14+17\,k,2+2\,k,-5-6\,k]] {\it PISOT} \left( 17,289\,k+241 \right) =[[17,289\,k+241,4913\,{k}^{2} +8194\,k+3417],[15+17\,k,-12-14\,k,5+6\,k]] {\it PISOT} \left( 17,289\,k+242 \right) =[[17,289\,k+242,4913\,{k}^{2} +8228\,k+3445],[14+17\,k,3+4\,k,5+6\,k]] {\it PISOT} \left( 17,289\,k+244 \right) =[[17,289\,k+244,4913\,{k}^{2} +8296\,k+3502,83521\,{k}^{3}+211548\,{k}^{2}+178604\,k+50262],[15+17\,k ,-9-11\,k,-5-5\,k,11+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.979539819317329 {\it PISOT} \left( 17,289\,k+245 \right) =[[17,289\,k+245,4913\,{k}^{2} +8330\,k+3531,83521\,{k}^{3}+212415\,{k}^{2}+180079\,k+50890,1419857\,{ k}^{4}+4814740\,{k}^{3}+6122652\,{k}^{2}+3460450\,k+733444,24137569\,{k }^{5}+102313225\,{k}^{4}+173474562\,{k}^{3}+147067445\,{k}^{2}+62341157 \,k+10570645],[14+17\,k,6+7\,k,-1-k,3+3\,k,-6-8\,k,-11-13\,k]] {\it PISOT} \left( 17,289\,k+248 \right) =[[17,289\,k+248],[15+17\,k,-6 -7\,k]] {\it PISOT} \left( 17,289\,k+249 \right) =[[17,289\,k+249,4913\,{k}^{2} +8466\,k+3647,83521\,{k}^{3}+215883\,{k}^{2}+185999\,k+53416,1419857\,{ k}^{4}+4893348\,{k}^{3}+6324000\,{k}^{2}+3632350\,k+782361],[15+17\,k,- 5-6\,k,-2-3\,k,-9-10\,k,6+7\,k]] {\it PISOT} \left( 17,289\,k+253 \right) =[[17,289\,k+253,4913\,{k}^{2} +8602\,k+3765,83521\,{k}^{3}+219351\,{k}^{2}+192019\,k+56029],[15+17\,k ,-2-2\,k,4+4\,k,-7-8\,k]] {\it PISOT} \left( 17,289\,k+257 \right) =[[17,289\,k+257,4913\,{k}^{2} +8738\,k+3885,83521\,{k}^{3}+222819\,{k}^{2}+198139\,k+58729],[15+17\,k ,2+2\,k,-3-4\,k,-8-9\,k]] {\it PISOT} \left( 17,289\,k+258 \right) =[[17,289\,k+258,4913\,{k}^{2} +8772\,k+3916],[16+17\,k,-13-14\,k,8+9\,k]] {\it PISOT} \left( 17,289\,k+259 \right) =[[17,289\,k+259,4913\,{k}^{2} +8806\,k+3946,83521\,{k}^{3}+224553\,{k}^{2}+201245\,k+60119,1419857\,{ k}^{4}+5089868\,{k}^{3}+6842313\,{k}^{2}+4088074\,k+915939],[16+17\,k,- 12-13\,k,5+6\,k,6+6\,k,-9-10\,k]] {\it PISOT} \left( 17,289\,k+270 \right) =[[17,289\,k+270],[15+17\,k,14 +15\,k]] {\it PISOT} \left( 17,289\,k+271 \right) =[[17,289\,k+271],[15+17\,k,15 +16\,k]] {\it PISOT} \left( 17,289\,k+278 \right) =[[17,289\,k+278,4913\,{k}^{2} +9452\,k+4546,83521\,{k}^{3}+241026\,{k}^{2}+231848\,k+74339,1419857\,{ k}^{4}+5463256\,{k}^{3}+7882866\,{k}^{2}+5055102\,k+1215637,24137569\,{ k}^{5}+116094190\,{k}^{4}+223348448\,{k}^{3}+214843241\,{k}^{2}+ 103330258\,k+19878843],[17+17\,k,-11-11\,k,7+7\,k,-4-4\,k,2+2\,k,-1-k]] {\it PISOT} \left( 17,289\,k+280 \right) =[[17,289\,k+280,4913\,{k}^{2} +9520\,k+4612,83521\,{k}^{3}+242760\,{k}^{2}+235208\,k+75966,1419857\,{ k}^{4}+5502560\,{k}^{3}+7997004\,{k}^{2}+5165564\,k+1251265,24137569\,{ k}^{5}+116929400\,{k}^{4}+226580624\,{k}^{3}+219533242\,{k}^{2}+ 106354514\,k+20610064],[16+17\,k,8+8\,k,-4-4\,k,2+2\,k,-1-k,1+k]] {\it PISOT} \left( 17,289\,k+281 \right) =[[17,289\,k+281,4913\,{k}^{2} +9554\,k+4645,83521\,{k}^{3}+243627\,{k}^{2}+236891\,k+76783,1419857\,{ k}^{4}+5522212\,{k}^{3}+8054226\,{k}^{2}+5221112\,k+1269242],[17+17\,k, -8-8\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 17,289\,k+282 \right) =[[17,289\,k+282,4913\,{k}^{2} +9588\,k+4678,83521\,{k}^{3}+244494\,{k}^{2}+238576\,k+77602],[17+17\,k ,-7-7\,k,3+3\,k,-1-k]] {\it PISOT} \left( 17,289\,k+283 \right) =[[17,289\,k+283,4913\,{k}^{2} +9622\,k+4711,83521\,{k}^{3}+245361\,{k}^{2}+240263\,k+78422],[17+17\,k ,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 17,289\,k+284 \right) =[[17,289\,k+284,4913\,{k}^{2} +9656\,k+4744],[17+17\,k,-5-5\,k,1+k]] {\it PISOT} \left( 17,289\,k+285 \right) =[[17,289\,k+285,4913\,{k}^{2} +9690\,k+4778],[17+17\,k,-4-4\,k,1+k]] {\it PISOT} \left( 17,289\,k+286 \right) =[[17,289\,k+286,4913\,{k}^{2} +9724\,k+4812],[17+17\,k,-3-3\,k,1+k]] {\it PISOT} \left( 17,289\,k+287 \right) =[[17,289\,k+287],[17+17\,k,-2 -2\,k]] {\it PISOT} \left( 17,289\,k+288 \right) =[[17,289\,k+288],[17+17\,k,-1 -k]] {\it PISOT} \left( 18,324\,k+1 \right) =[[18,324\,k+1],[18\,k,k]] {\it PISOT} \left( 18,324\,k+2 \right) =[[18,324\,k+2],[18\,k,2\,k]] {\it PISOT} \left( 18,324\,k+3 \right) =[[18,324\,k+3,5832\,{k}^{2}+108 \,k+1],[18\,k,3\,k,k]] {\it PISOT} \left( 18,324\,k+4 \right) =[[18,324\,k+4,5832\,{k}^{2}+144 \,k+1],[18\,k,4\,k,k]] {\it PISOT} \left( 18,324\,k+5 \right) =[[18,324\,k+5,5832\,{k}^{2}+180 \,k+1],[18\,k,5\,k,k]] {\it PISOT} \left( 18,324\,k+6 \right) =[[18,324\,k+6,5832\,{k}^{2}+216 \,k+2,104976\,{k}^{3}+5832\,{k}^{2}+108\,k+1],[18\,k,6\,k,2\,k,k]] {\it PISOT} \left( 18,324\,k+7 \right) =[[18,324\,k+7,5832\,{k}^{2}+252 \,k+3,104976\,{k}^{3}+6804\,{k}^{2}+157\,k+1],[18\,k,7\,k,3\,k,k]] {\it PISOT} \left( 18,324\,k+8 \right) =[[18,324\,k+8,5832\,{k}^{2}+288 \,k+4,104976\,{k}^{3}+7776\,{k}^{2}+208\,k+2,1889568\,{k}^{4}+186624\,{ k}^{3}+7344\,{k}^{2}+136\,k+1],[18\,k,8\,k,4\,k,2\,k,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970419968581249 {\it PISOT} \left( 18,324\,k+9 \right) =[[18,324\,k+9,5832\,{k}^{2}+324 \,k+5,104976\,{k}^{3}+8748\,{k}^{2}+261\,k+3,1889568\,{k}^{4}+209952\,{ k}^{3}+9234\,{k}^{2}+198\,k+2,34012224\,{k}^{5}+4723920\,{k}^{4}+274104 \,{k}^{3}+8505\,{k}^{2}+151\,k+1],[1+18\,k,-9\,k,-4\,k,-2\,k,-k,-k]] {\it PISOT} \left( 18,324\,k+11 \right) =[[18,324\,k+11,5832\,{k}^{2}+ 396\,k+7,104976\,{k}^{3}+10692\,{k}^{2}+373\,k+4,1889568\,{k}^{4}+ 256608\,{k}^{3}+13338\,{k}^{2}+298\,k+2,34012224\,{k}^{5}+5773680\,{k}^ {4}+398520\,{k}^{3}+13535\,{k}^{2}+209\,k+1],[18\,k,11\,k,7\,k,4\,k,2\, k,k]] {\it PISOT} \left( 18,324\,k+19 \right) =[[18,324\,k+19],[2+18\,k,-1-17 \,k]] {\it PISOT} \left( 18,324\,k+20 \right) =[[18,324\,k+20],[2+18\,k,-1-16 \,k]] {\it PISOT} \left( 18,324\,k+29 \right) =[[18,324\,k+29],[1+18\,k,1+11 \,k]] {\it PISOT} \left( 18,324\,k+39 \right) =[[18,324\,k+39,5832\,{k}^{2}+ 1404\,k+85,104976\,{k}^{3}+37908\,{k}^{2}+4581\,k+185],[3+18\,k,-2-15\, k,4\,k,1+8\,k]] {\it PISOT} \left( 18,324\,k+41 \right) =[[18,324\,k+41,5832\,{k}^{2}+ 1476\,k+93],[1+18\,k,2+23\,k,2+16\,k]] {\it PISOT} \left( 18,324\,k+46 \right) =[[18,324\,k+46,5832\,{k}^{2}+ 1656\,k+118,104976\,{k}^{3}+44712\,{k}^{2}+6364\,k+303],[2+18\,k,2+10\, k,-1-10\,k,-1-7\,k]] {\it PISOT} \left( 18,324\,k+47 \right) =[[18,324\,k+47],[3+18\,k,-1-7 \,k]] {\it PISOT} \left( 18,324\,k+55 \right) =[[18,324\,k+55,5832\,{k}^{2}+ 1980\,k+168,104976\,{k}^{3}+53460\,{k}^{2}+9073\,k+513],[4+18\,k,-3-17 \,k,2\,k,1+6\,k]] {\it PISOT} \left( 18,324\,k+59 \right) =[[18,324\,k+59,5832\,{k}^{2}+ 2124\,k+193],[4+18\,k,-3-13\,k,2+11\,k]] {\it PISOT} \left( 18,324\,k+64 \right) =[[18,324\,k+64],[3+18\,k,2+10 \,k]] {\it PISOT} \left( 18,324\,k+65 \right) =[[18,324\,k+65,5832\,{k}^{2}+ 2340\,k+235,104976\,{k}^{3}+63180\,{k}^{2}+12685\,k+850,1889568\,{k}^{4 }+1516320\,{k}^{3}+456570\,{k}^{2}+61150\,k+3074],[4+18\,k,-1-7\,k,-1-7 \,k,-2-7\,k,2+10\,k]] {\it PISOT} \left( 18,324\,k+75 \right) =[[18,324\,k+75,5832\,{k}^{2}+ 2700\,k+313],[4+18\,k,3\,k,3+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.9718266826 {\it PISOT} \left( 18,324\,k+76 \right) =[[18,324\,k+76,5832\,{k}^{2}+ 2736\,k+321],[4+18\,k,4\,k,4+17\,k]] {\it PISOT} \left( 18,324\,k+79 \right) =[[18,324\,k+79,5832\,{k}^{2}+ 2844\,k+347,104976\,{k}^{3}+76788\,{k}^{2}+18733\,k+1524],[4+18\,k,2+7 \,k,-1-5\,k,-1-4\,k]] {\it PISOT} \left( 18,324\,k+80 \right) =[[18,324\,k+80],[4+18\,k,2+8\, k]] {\it PISOT} \left( 18,324\,k+81 \right) =[[18,324\,k+81,5832\,{k}^{2}+ 2916\,k+365],[5+18\,k,-2-9\,k,-1-4\,k]] {\it PISOT} \left( 18,324\,k+82 \right) =[[18,324\,k+82],[5+18\,k,-2-8 \,k]] {\it PISOT} \left( 18,324\,k+83 \right) =[[18,324\,k+83,5832\,{k}^{2}+ 2988\,k+383],[5+18\,k,-2-7\,k,1+4\,k]] {\it PISOT} \left( 18,324\,k+84 \right) =[[18,324\,k+84,5832\,{k}^{2}+ 3024\,k+392,104976\,{k}^{3}+81648\,{k}^{2}+21168\,k+1829,1889568\,{k}^{ 4}+1959552\,{k}^{3}+762048\,{k}^{2}+131700\,k+8534],[6+18\,k,-7-24\,k,4 +14\,k,-2-7\,k,1+4\,k]] {\it PISOT} \left( 18,324\,k+89 \right) =[[18,324\,k+89,5832\,{k}^{2}+ 3204\,k+440,104976\,{k}^{3}+86508\,{k}^{2}+23761\,k+2175],[5+18\,k,-k,- 2-5\,k,3+11\,k]] {\it PISOT} \left( 18,324\,k+92 \right) =[[18,324\,k+92,5832\,{k}^{2}+ 3312\,k+470,104976\,{k}^{3}+89424\,{k}^{2}+25384\,k+2401],[4+18\,k,5+20 \,k,3+12\,k,2+7\,k]] {\it PISOT} \left( 18,324\,k+98 \right) =[[18,324\,k+98],[6+18\,k,-3-10 \,k]] {\it PISOT} \left( 18,324\,k+103 \right) =[[18,324\,k+103,5832\,{k}^{2} +3708\,k+589,104976\,{k}^{3}+100116\,{k}^{2}+31813\,k+3368,1889568\,{k} ^{4}+2402784\,{k}^{3}+1145394\,{k}^{2}+242582\,k+19259,34012224\,{k}^{5 }+54062640\,{k}^{4}+34364088\,{k}^{3}+10918459\,{k}^{2}+1734053\,k+ 110127],[5+18\,k,4+13\,k,2\,k,3+11\,k,3+9\,k,-1-3\,k]] {\it PISOT} \left( 18,324\,k+104 \right) =[[18,324\,k+104,5832\,{k}^{2} +3744\,k+601,104976\,{k}^{3}+101088\,{k}^{2}+32452\,k+3473,1889568\,{k} ^{4}+2426112\,{k}^{3}+1168236\,{k}^{2}+250036\,k+20069],[5+18\,k,5+14\, k,-2-9\,k,-5-16\,k,-1-3\,k]] {\it PISOT} \left( 18,324\,k+106 \right) =[[18,324\,k+106,5832\,{k}^{2} +3816\,k+624,104976\,{k}^{3}+103032\,{k}^{2}+33700\,k+3673,1889568\,{k} ^{4}+2472768\,{k}^{3}+1213272\,{k}^{2}+264516\,k+21620],[6+18\,k,-2\,k, -4-12\,k,k,2+6\,k]] {\it PISOT} \left( 18,324\,k+107 \right) =[[18,324\,k+107,5832\,{k}^{2} +3852\,k+636],[6+18\,k,-k,-2-6\,k]] {\it PISOT} \left( 18,324\,k+109 \right) =[[18,324\,k+109,5832\,{k}^{2} +3924\,k+660],[6+18\,k,k,2+6\,k]] {\it PISOT} \left( 18,324\,k+110 \right) =[[18,324\,k+110,5832\,{k}^{2} +3960\,k+672,104976\,{k}^{3}+106920\,{k}^{2}+36292\,k+4105,1889568\,{k} ^{4}+2566080\,{k}^{3}+1306584\,{k}^{2}+295620\,k+25076],[6+18\,k,2\,k,4 +12\,k,k,2+6\,k]] {\it PISOT} \left( 18,324\,k+112 \right) =[[18,324\,k+112,5832\,{k}^{2} +4032\,k+697,104976\,{k}^{3}+108864\,{k}^{2}+37636\,k+4338],[5+18\,k,7+ 22\,k,4+11\,k,-1-3\,k]] {\it PISOT} \left( 18,324\,k+116 \right) =[[18,324\,k+116,5832\,{k}^{2} +4176\,k+748,104976\,{k}^{3}+112752\,{k}^{2}+40384\,k+4823,1889568\,{k} ^{4}+2706048\,{k}^{3}+1453680\,{k}^{2}+347164\,k+31098],[6+18\,k,3+8\,k ,-1-2\,k,1+5\,k,5+14\,k]] {\it PISOT} \left( 18,324\,k+128 \right) =[[18,324\,k+128,5832\,{k}^{2} +4608\,k+910,104976\,{k}^{3}+124416\,{k}^{2}+49144\,k+6470,1889568\,{k} ^{4}+2985984\,{k}^{3}+1769256\,{k}^{2}+465880\,k+46001],[8+18\,k,-6-16 \,k,-3-6\,k,5+12\,k,-2-5\,k]] {\it PISOT} \left( 18,324\,k+130 \right) =[[18,324\,k+130,5832\,{k}^{2} +4680\,k+939],[6+18\,k,8+22\,k,6+15\,k]] {\it PISOT} \left( 18,324\,k+131 \right) =[[18,324\,k+131],[7+18\,k,2+5 \,k]] {\it PISOT} \left( 18,324\,k+135 \right) =[[18,324\,k+135,5832\,{k}^{2} +4860\,k+1013,104976\,{k}^{3}+131220\,{k}^{2}+54693\,k+7601],[7+18\,k,4 +9\,k,-1-4\,k,-5-12\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.980531854461797 {\it PISOT} \left( 18,324\,k+137 \right) =[[18,324\,k+137,5832\,{k}^{2} +4932\,k+1043,104976\,{k}^{3}+133164\,{k}^{2}+56317\,k+7941,1889568\,{k }^{4}+3195936\,{k}^{3}+2027322\,{k}^{2}+571658\,k+60460,34012224\,{k}^{ 5}+71908560\,{k}^{4}+60818040\,{k}^{3}+25722233\,{k}^{2}+5440243\,k+ 460321],[8+18\,k,-4-7\,k,8+19\,k,k,3+8\,k,3+7\,k]] {\it PISOT} \left( 18,324\,k+138 \right) =[[18,324\,k+138,5832\,{k}^{2} +4968\,k+1058,104976\,{k}^{3}+134136\,{k}^{2}+57132\,k+8111],[8+18\,k,- 3-6\,k,3+8\,k,3+7\,k]] {\it PISOT} \left( 18,324\,k+140 \right) =[[18,324\,k+140,5832\,{k}^{2} +5040\,k+1089,104976\,{k}^{3}+136080\,{k}^{2}+58804\,k+8471],[8+18\,k,- 1-4\,k,-6-13\,k,3+7\,k]] {\it PISOT} \left( 18,324\,k+142 \right) =[[18,324\,k+142],[7+18\,k,7+ 16\,k]] {\it PISOT} \left( 18,324\,k+143 \right) =[[18,324\,k+143,5832\,{k}^{2} +5148\,k+1136,104976\,{k}^{3}+138996\,{k}^{2}+61345\,k+9024,1889568\,{k }^{4}+3335904\,{k}^{3}+2208438\,{k}^{2}+649760\,k+71684],[7+18\,k,7+17 \,k,3+9\,k,7+17\,k,4+9\,k]] {\it PISOT} \left( 18,324\,k+145 \right) =[[18,324\,k+145,5832\,{k}^{2} +5220\,k+1168],[7+18\,k,8+19\,k,4+9\,k]] {\it PISOT} \left( 18,324\,k+147 \right) =[[18,324\,k+147,5832\,{k}^{2} +5292\,k+1201],[8+18\,k,2+3\,k,-5-11\,k]] {\it PISOT} \left( 18,324\,k+148 \right) =[[18,324\,k+148,5832\,{k}^{2} +5328\,k+1217],[9+18\,k,-7-14\,k,5+11\,k]] {\it PISOT} \left( 18,324\,k+149 \right) =[[18,324\,k+149],[9+18\,k,-6- 13\,k]] {\it PISOT} \left( 18,324\,k+153 \right) =[[18,324\,k+153,5832\,{k}^{2} +5508\,k+1301,104976\,{k}^{3}+148716\,{k}^{2}+70245\,k+11063,1889568\,{ k}^{4}+3569184\,{k}^{3}+2528658\,{k}^{2}+796374\,k+94074,34012224\,{k}^ {5}+80306640\,{k}^{4}+75856824\,{k}^{3}+35832537\,{k}^{2}+8464543\,k+ 799956],[9+18\,k,-5-9\,k,7+14\,k,-4-7\,k,6+13\,k,1+2\,k]] {\it PISOT} \left( 18,324\,k+156 \right) =[[18,324\,k+156,5832\,{k}^{2} +5616\,k+1352,104976\,{k}^{3}+151632\,{k}^{2}+73008\,k+11717,1889568\,{ k}^{4}+3639168\,{k}^{3}+2628288\,{k}^{2}+843636\,k+101544,34012224\,{k} ^{5}+81881280\,{k}^{4}+78848640\,{k}^{3}+37963836\,{k}^{2}+9139192\,k+ 880019],[8+18\,k,5+12\,k,6+14\,k,6+13\,k,2+4\,k,-1-2\,k]] {\it PISOT} \left( 18,324\,k+157 \right) =[[18,324\,k+157,5832\,{k}^{2} +5652\,k+1369,104976\,{k}^{3}+152604\,{k}^{2}+73933\,k+11937],[9+18\,k, -2-5\,k,-4-8\,k,1+2\,k]] {\it PISOT} \left( 18,324\,k+158 \right) =[[18,324\,k+158,5832\,{k}^{2} +5688\,k+1387,104976\,{k}^{3}+153576\,{k}^{2}+74896\,k+12176,1889568\,{ k}^{4}+3685824\,{k}^{3}+2696220\,{k}^{2}+876628\,k+106889],[8+18\,k,7+ 14\,k,-1-3\,k,-4-8\,k,1+2\,k]] {\it PISOT} \left( 18,324\,k+160 \right) =[[18,324\,k+160],[9+18\,k,-1- 2\,k]] {\it PISOT} \left( 18,324\,k+161 \right) =[[18,324\,k+161,5832\,{k}^{2} +5796\,k+1440],[8+18\,k,8+17\,k,4+8\,k]] {\it PISOT} \left( 18,324\,k+163 \right) =[[18,324\,k+163,5832\,{k}^{2} +5868\,k+1476],[10+18\,k,-9-17\,k,4+8\,k]] {\it PISOT} \left( 18,324\,k+164 \right) =[[18,324\,k+164],[9+18\,k,1+2 \,k]] {\it PISOT} \left( 18,324\,k+166 \right) =[[18,324\,k+166,5832\,{k}^{2} +5976\,k+1531,104976\,{k}^{3}+161352\,{k}^{2}+82672\,k+14120,1889568\,{ k}^{4}+3872448\,{k}^{3}+2976156\,{k}^{2}+1016612\,k+130225],[10+18\,k,- 7-14\,k,-2-3\,k,4+8\,k,1+2\,k]] {\it PISOT} \left( 18,324\,k+167 \right) =[[18,324\,k+167,5832\,{k}^{2} +6012\,k+1549,104976\,{k}^{3}+162324\,{k}^{2}+83653\,k+14368],[9+18\,k, 3+5\,k,-4-8\,k,-1-2\,k]] {\it PISOT} \left( 18,324\,k+168 \right) =[[18,324\,k+168,5832\,{k}^{2} +6048\,k+1568,104976\,{k}^{3}+163296\,{k}^{2}+84672\,k+14635,1889568\,{ k}^{4}+3919104\,{k}^{3}+3048192\,{k}^{2}+1053708\,k+136596,34012224\,{k }^{5}+88179840\,{k}^{4}+91445760\,{k}^{3}+47416644\,{k}^{2}+12293440\,k +1274921],[10+18\,k,-7-12\,k,8+14\,k,-7-13\,k,2+4\,k,1+2\,k]] {\it PISOT} \left( 18,324\,k+171 \right) =[[18,324\,k+171,5832\,{k}^{2} +6156\,k+1625,104976\,{k}^{3}+166212\,{k}^{2}+87741\,k+15442,1889568\,{ k}^{4}+3989088\,{k}^{3}+3158514\,{k}^{2}+1111662\,k+146742,34012224\,{k }^{5}+89754480\,{k}^{4}+94752504\,{k}^{3}+50020335\,{k}^{2}+13204501\,k +1394458],[9+18\,k,4+9\,k,7+14\,k,3+7\,k,7+13\,k,-1-2\,k]] {\it PISOT} \left( 18,324\,k+175 \right) =[[18,324\,k+175],[9+18\,k,7+ 13\,k]] {\it PISOT} \left( 18,324\,k+176 \right) =[[18,324\,k+176,5832\,{k}^{2} +6336\,k+1721],[9+18\,k,7+14\,k,6+11\,k]] {\it PISOT} \left( 18,324\,k+177 \right) =[[18,324\,k+177,5832\,{k}^{2} +6372\,k+1741],[10+18\,k,-1-3\,k,-6-11\,k]] {\it PISOT} \left( 18,324\,k+179 \right) =[[18,324\,k+179,5832\,{k}^{2} +6444\,k+1780],[11+18\,k,-11-19\,k,5+9\,k]] {\it PISOT} \left( 18,324\,k+181 \right) =[[18,324\,k+181,5832\,{k}^{2} +6516\,k+1820,104976\,{k}^{3}+175932\,{k}^{2}+98281\,k+18301,1889568\,{ k}^{4}+4222368\,{k}^{3}+3538134\,{k}^{2}+1317676\,k+184026],[11+18\,k,- 10-17\,k,6+9\,k,-10-17\,k,5+9\,k]] {\it PISOT} \left( 18,324\,k+182 \right) =[[18,324\,k+182],[11+18\,k,-9 -16\,k]] {\it PISOT} \left( 18,324\,k+184 \right) =[[18,324\,k+184,5832\,{k}^{2} +6624\,k+1881,104976\,{k}^{3}+178848\,{k}^{2}+101572\,k+19229],[10+18\, k,3+4\,k,-7-13\,k,-4-7\,k]] {\it PISOT} \left( 18,324\,k+186 \right) =[[18,324\,k+186,5832\,{k}^{2} +6696\,k+1922,104976\,{k}^{3}+180792\,{k}^{2}+103788\,k+19861],[10+18\, k,3+6\,k,5+8\,k,-4-7\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.980530974227514 {\it PISOT} \left( 18,324\,k+187 \right) =[[18,324\,k+187,5832\,{k}^{2} +6732\,k+1943,104976\,{k}^{3}+181764\,{k}^{2}+104917\,k+20188,1889568\, {k}^{4}+4362336\,{k}^{3}+3776922\,{k}^{2}+1453450\,k+209756,34012224\,{ k}^{5}+98152560\,{k}^{4}+113306040\,{k}^{3}+65402767\,{k}^{2}+18876777 \,k+2179393],[10+18\,k,3+7\,k,11+19\,k,-1-k,5+8\,k,-4-7\,k]] {\it PISOT} \left( 18,324\,k+189 \right) =[[18,324\,k+189,5832\,{k}^{2} +6804\,k+1985,104976\,{k}^{3}+183708\,{k}^{2}+107181\,k+20848],[11+18\, k,-5-9\,k,-3-4\,k,7+12\,k]] {\it PISOT} \left( 18,324\,k+193 \right) =[[18,324\,k+193],[11+18\,k,-3 -5\,k]] {\it PISOT} \left( 18,324\,k+194 \right) =[[18,324\,k+194,5832\,{k}^{2} +6984\,k+2091],[12+18\,k,-14-22\,k,9+15\,k]] {\it PISOT} \left( 18,324\,k+196 \right) =[[18,324\,k+196,5832\,{k}^{2} +7056\,k+2134,104976\,{k}^{3}+190512\,{k}^{2}+115240\,k+23234,1889568\, {k}^{4}+4572288\,{k}^{3}+4148712\,{k}^{2}+1672952\,k+252961],[10+18\,k, 10+16\,k,-3-6\,k,-7-12\,k,-3-5\,k]] {\it PISOT} \left( 18,324\,k+208 \right) =[[18,324\,k+208,5832\,{k}^{2} +7488\,k+2404,104976\,{k}^{3}+202176\,{k}^{2}+129808\,k+27785,1889568\, {k}^{4}+4852224\,{k}^{3}+4672944\,{k}^{2}+2000324\,k+321134],[12+18\,k, -5-8\,k,-1-2\,k,-4-5\,k,9+14\,k]] {\it PISOT} \left( 18,324\,k+212 \right) =[[18,324\,k+212,5832\,{k}^{2} +7632\,k+2497,104976\,{k}^{3}+206064\,{k}^{2}+134836\,k+29410],[13+18\, k,-15-22\,k,7+11\,k,2+3\,k]] {\it PISOT} \left( 18,324\,k+214 \right) =[[18,324\,k+214,5832\,{k}^{2} +7704\,k+2544,104976\,{k}^{3}+208008\,{k}^{2}+137380\,k+30243,1889568\, {k}^{4}+4992192\,{k}^{3}+4945752\,{k}^{2}+2177580\,k+359528],[12+18\,k, -2-2\,k,8+12\,k,-1-k,4+6\,k]] {\it PISOT} \left( 18,324\,k+215 \right) =[[18,324\,k+215,5832\,{k}^{2} +7740\,k+2568],[12+18\,k,-1-k,4+6\,k]] {\it PISOT} \left( 18,324\,k+217 \right) =[[18,324\,k+217,5832\,{k}^{2} +7812\,k+2616],[12+18\,k,1+k,-4-6\,k]] {\it PISOT} \left( 18,324\,k+218 \right) =[[18,324\,k+218,5832\,{k}^{2} +7848\,k+2640,104976\,{k}^{3}+211896\,{k}^{2}+142564\,k+31971,1889568\, {k}^{4}+5085504\,{k}^{3}+5132376\,{k}^{2}+2301996\,k+387176],[12+18\,k, 2+2\,k,-8-12\,k,-1-k,4+6\,k]] {\it PISOT} \left( 18,324\,k+220 \right) =[[18,324\,k+220,5832\,{k}^{2} +7920\,k+2689,104976\,{k}^{3}+213840\,{k}^{2}+145204\,k+32867,1889568\, {k}^{4}+5132160\,{k}^{3}+5227308\,{k}^{2}+2366372\,k+401725],[13+18\,k, -9-14\,k,-7-9\,k,11+16\,k,-2-3\,k]] {\it PISOT} \left( 18,324\,k+221 \right) =[[18,324\,k+221,5832\,{k}^{2} +7956\,k+2713,104976\,{k}^{3}+214812\,{k}^{2}+146509\,k+33305,1889568\, {k}^{4}+5155488\,{k}^{3}+5274450\,{k}^{2}+2398126\,k+408855,34012224\,{ k}^{5}+115998480\,{k}^{4}+158235768\,{k}^{3}+107920205\,{k}^{2}+ 36799959\,k+5019139],[13+18\,k,-9-13\,k,2+2\,k,-8-11\,k,6+9\,k,2+3\,k]] {\it PISOT} \left( 18,324\,k+226 \right) =[[18,324\,k+226],[12+18\,k,7+ 10\,k]] {\it PISOT} \left( 18,324\,k+232 \right) =[[18,324\,k+232,5832\,{k}^{2} +8352\,k+2990,104976\,{k}^{3}+225504\,{k}^{2}+161464\,k+38535],[14+18\, k,-15-20\,k,9+12\,k,-5-7\,k]] {\it PISOT} \left( 18,324\,k+235 \right) =[[18,324\,k+235,5832\,{k}^{2} +8460\,k+3068,104976\,{k}^{3}+228420\,{k}^{2}+165673\,k+40054],[13+18\, k,1+k,-3-5\,k,-8-11\,k]] {\it PISOT} \left( 18,324\,k+240 \right) =[[18,324\,k+240,5832\,{k}^{2} +8640\,k+3200,104976\,{k}^{3}+233280\,{k}^{2}+172800\,k+42667,1889568\, {k}^{4}+5598720\,{k}^{3}+6220800\,{k}^{2}+3072012\,k+568898],[12+18\,k, 17+24\,k,10+14\,k,5+7\,k,3+4\,k]] {\it PISOT} \left( 18,324\,k+241 \right) =[[18,324\,k+241,5832\,{k}^{2} +8676\,k+3227],[13+18\,k,5+7\,k,3+4\,k]] {\it PISOT} \left( 18,324\,k+242 \right) =[[18,324\,k+242],[13+18\,k,6+ 8\,k]] {\it PISOT} \left( 18,324\,k+243 \right) =[[18,324\,k+243,5832\,{k}^{2} +8748\,k+3281],[13+18\,k,7+9\,k,-3-4\,k]] {\it PISOT} \left( 18,324\,k+244 \right) =[[18,324\,k+244],[14+18\,k,-6 -8\,k]] {\it PISOT} \left( 18,324\,k+245 \right) =[[18,324\,k+245,5832\,{k}^{2} +8820\,k+3335,104976\,{k}^{3}+238140\,{k}^{2}+180085\,k+45397],[14+18\, k,-5-7\,k,-4-5\,k,3+4\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.9718257080 {\it PISOT} \left( 18,324\,k+248 \right) =[[18,324\,k+248,5832\,{k}^{2} +8928\,k+3417],[14+18\,k,-4-4\,k,13+17\,k]] {\it PISOT} \left( 18,324\,k+249 \right) =[[18,324\,k+249,5832\,{k}^{2} +8964\,k+3445],[14+18\,k,-3-3\,k,10+13\,k]] {\it PISOT} \left( 18,324\,k+259 \right) =[[18,324\,k+259,5832\,{k}^{2} +9324\,k+3727,104976\,{k}^{3}+251748\,{k}^{2}+201253\,k+53631,1889568\, {k}^{4}+6041952\,{k}^{3}+7245018\,{k}^{2}+3861302\,k+771742],[14+18\,k, 6+7\,k,-6-7\,k,5+7\,k,8+10\,k]] {\it PISOT} \left( 18,324\,k+260 \right) =[[18,324\,k+260],[15+18\,k,-8 -10\,k]] {\it PISOT} \left( 18,324\,k+265 \right) =[[18,324\,k+265,5832\,{k}^{2} +9540\,k+3901],[14+18\,k,10+13\,k,9+11\,k]] {\it PISOT} \left( 18,324\,k+269 \right) =[[18,324\,k+269,5832\,{k}^{2} +9684\,k+4020,104976\,{k}^{3}+261468\,{k}^{2}+217081\,k+60076],[14+18\, k,14+17\,k,2+2\,k,-5-6\,k]] {\it PISOT} \left( 18,324\,k+277 \right) =[[18,324\,k+277],[15+18\,k,6+ 7\,k]] {\it PISOT} \left( 18,324\,k+278 \right) =[[18,324\,k+278,5832\,{k}^{2} +10008\,k+4294,104976\,{k}^{3}+270216\,{k}^{2}+231868\,k+66325],[16+18 \,k,-8-10\,k,-9-10\,k,6+7\,k]] {\it PISOT} \left( 18,324\,k+283 \right) =[[18,324\,k+283,5832\,{k}^{2} +10188\,k+4449],[17+18\,k,-21-23\,k,14+16\,k]] {\it PISOT} \left( 18,324\,k+285 \right) =[[18,324\,k+285,5832\,{k}^{2} +10260\,k+4513,104976\,{k}^{3}+277020\,{k}^{2}+243693\,k+71464],[15+18 \,k,13+15\,k,4+4\,k,-7-8\,k]] {\it PISOT} \left( 18,324\,k+295 \right) =[[18,324\,k+295],[17+18\,k,- 10-11\,k]] {\it PISOT} \left( 18,324\,k+304 \right) =[[18,324\,k+304],[16+18\,k,15 +16\,k]] {\it PISOT} \left( 18,324\,k+305 \right) =[[18,324\,k+305],[16+18\,k,16 +17\,k]] {\it PISOT} \left( 18,324\,k+313 \right) =[[18,324\,k+313,5832\,{k}^{2} +11268\,k+5443,104976\,{k}^{3}+304236\,{k}^{2}+293917\,k+94653,1889568 \,{k}^{4}+7301664\,{k}^{3}+10580922\,{k}^{2}+6814826\,k+1646002, 34012224\,{k}^{5}+164287440\,{k}^{4}+317426040\,{k}^{3}+306662185\,{k}^ {2}+148135099\,k+28623737],[18+18\,k,-11-11\,k,7+7\,k,-4-4\,k,2+2\,k,-1 -k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970421624309967 {\it PISOT} \left( 18,324\,k+315 \right) =[[18,324\,k+315,5832\,{k}^{2} +11340\,k+5513,104976\,{k}^{3}+306180\,{k}^{2}+297693\,k+96486,1889568 \,{k}^{4}+7348320\,{k}^{3}+10716786\,{k}^{2}+6946686\,k+1688654, 34012224\,{k}^{5}+165337200\,{k}^{4}+321500664\,{k}^{3}+312592527\,{k}^ {2}+151970893\,k+29554053],[17+18\,k,9+9\,k,-4-4\,k,2+2\,k,-1-k,1+k]] {\it PISOT} \left( 18,324\,k+316 \right) =[[18,324\,k+316,5832\,{k}^{2} +11376\,k+5548,104976\,{k}^{3}+307152\,{k}^{2}+299584\,k+97406,1889568 \,{k}^{4}+7371648\,{k}^{3}+10784880\,{k}^{2}+7012952\,k+1710153],[18+18 \,k,-8-8\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 18,324\,k+317 \right) =[[18,324\,k+317,5832\,{k}^{2} +11412\,k+5583,104976\,{k}^{3}+308124\,{k}^{2}+301477\,k+98328],[18+18 \,k,-7-7\,k,3+3\,k,-1-k]] {\it PISOT} \left( 18,324\,k+318 \right) =[[18,324\,k+318,5832\,{k}^{2} +11448\,k+5618,104976\,{k}^{3}+309096\,{k}^{2}+303372\,k+99251],[18+18 \,k,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 18,324\,k+319 \right) =[[18,324\,k+319,5832\,{k}^{2} +11484\,k+5653],[18+18\,k,-5-5\,k,1+k]] {\it PISOT} \left( 18,324\,k+320 \right) =[[18,324\,k+320,5832\,{k}^{2} +11520\,k+5689],[18+18\,k,-4-4\,k,1+k]] {\it PISOT} \left( 18,324\,k+321 \right) =[[18,324\,k+321,5832\,{k}^{2} +11556\,k+5725],[18+18\,k,-3-3\,k,1+k]] {\it PISOT} \left( 18,324\,k+322 \right) =[[18,324\,k+322],[18+18\,k,-2 -2\,k]] {\it PISOT} \left( 18,324\,k+323 \right) =[[18,324\,k+323],[18+18\,k,-1 -k]] {\it PISOT} \left( 19,361\,k+1 \right) =[[19,361\,k+1],[19\,k,k]] {\it PISOT} \left( 19,361\,k+2 \right) =[[19,361\,k+2],[19\,k,2\,k]] {\it PISOT} \left( 19,361\,k+3 \right) =[[19,361\,k+3],[19\,k,3\,k]] {\it PISOT} \left( 19,361\,k+4 \right) =[[19,361\,k+4,6859\,{k}^{2}+152 \,k+1],[19\,k,4\,k,k]] {\it PISOT} \left( 19,361\,k+5 \right) =[[19,361\,k+5,6859\,{k}^{2}+190 \,k+1],[19\,k,5\,k,k]] {\it PISOT} \left( 19,361\,k+6 \right) =[[19,361\,k+6,6859\,{k}^{2}+228 \,k+2,130321\,{k}^{3}+6498\,{k}^{2}+112\,k+1],[19\,k,6\,k,2\,k,k]] {\it PISOT} \left( 19,361\,k+7 \right) =[[19,361\,k+7,6859\,{k}^{2}+266 \,k+3,130321\,{k}^{3}+7581\,{k}^{2}+163\,k+1],[19\,k,7\,k,3\,k,k]] {\it PISOT} \left( 19,361\,k+8 \right) =[[19,361\,k+8,6859\,{k}^{2}+304 \,k+3,130321\,{k}^{3}+8664\,{k}^{2}+178\,k+1],[19\,k,8\,k,3\,k,k]] {\it PISOT} \left( 19,361\,k+9 \right) =[[19,361\,k+9,6859\,{k}^{2}+342 \,k+4,130321\,{k}^{3}+9747\,{k}^{2}+233\,k+2,2476099\,{k}^{4}+246924\,{ k}^{3}+8949\,{k}^{2}+148\,k+1],[19\,k,9\,k,4\,k,2\,k,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970254721867615 {\it PISOT} \left( 19,361\,k+10 \right) =[[19,361\,k+10,6859\,{k}^{2}+ 380\,k+5,130321\,{k}^{3}+10830\,{k}^{2}+290\,k+2,2476099\,{k}^{4}+ 274360\,{k}^{3}+11115\,{k}^{2}+176\,k+1],[1+19\,k,-9\,k,-5\,k,-3\,k,-k] ] {\it PISOT} \left( 19,361\,k+11 \right) =[[19,361\,k+11,6859\,{k}^{2}+ 418\,k+6,130321\,{k}^{3}+11913\,{k}^{2}+349\,k+3,2476099\,{k}^{4}+ 301796\,{k}^{3}+13395\,{k}^{2}+246\,k+1],[19\,k,11\,k,6\,k,3\,k,k]] {\it PISOT} \left( 19,361\,k+20 \right) =[[19,361\,k+20],[2+19\,k,-1-18 \,k]] {\it PISOT} \left( 19,361\,k+21 \right) =[[19,361\,k+21],[2+19\,k,-1-17 \,k]] {\it PISOT} \left( 19,361\,k+22 \right) =[[19,361\,k+22],[2+19\,k,-1-16 \,k]] {\it PISOT} \left( 19,361\,k+26 \right) =[[19,361\,k+26,6859\,{k}^{2}+ 988\,k+36,130321\,{k}^{3}+28158\,{k}^{2}+2044\,k+50],[1+19\,k,7\,k,10\, k,1+14\,k]] {\it PISOT} \left( 19,361\,k+28 \right) =[[19,361\,k+28,6859\,{k}^{2}+ 1064\,k+41],[1+19\,k,9\,k,1+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.977333144991208 {\it PISOT} \left( 19,361\,k+33 \right) =[[19,361\,k+33,6859\,{k}^{2}+ 1254\,k+57,130321\,{k}^{3}+35739\,{k}^{2}+3255\,k+98,2476099\,{k}^{4}+ 905388\,{k}^{3}+123804\,{k}^{2}+7486\,k+168,47045881\,{k}^{5}+21502965 \,{k}^{4}+3922626\,{k}^{3}+356505\,{k}^{2}+16101\,k+288],[1+19\,k,1+14 \,k,5\,k,1+8\,k,-6\,k,-1-11\,k]] {\it PISOT} \left( 19,361\,k+41 \right) =[[19,361\,k+41,6859\,{k}^{2}+ 1558\,k+88],[1+19\,k,2+22\,k,1+9\,k]] {\it PISOT} \left( 19,361\,k+43 \right) =[[19,361\,k+43,6859\,{k}^{2}+ 1634\,k+97,130321\,{k}^{3}+46569\,{k}^{2}+5535\,k+219,2476099\,{k}^{4}+ 1179748\,{k}^{3}+210444\,{k}^{2}+16664\,k+494,47045881\,{k}^{5}+ 28019015\,{k}^{4}+6666226\,{k}^{3}+792178\,{k}^{2}+47015\,k+1114],[3+19 \,k,-3-14\,k,4+25\,k,-3-19\,k,2+13\,k,-1-8\,k]] {\it PISOT} \left( 19,361\,k+46 \right) =[[19,361\,k+46],[2+19\,k,1+8\, k]] {\it PISOT} \left( 19,361\,k+48 \right) =[[19,361\,k+48,6859\,{k}^{2}+ 1824\,k+121],[3+19\,k,-2-9\,k,2+15\,k]] {\it PISOT} \left( 19,361\,k+52 \right) =[[19,361\,k+52],[2+19\,k,2+14 \,k]] {\it PISOT} \left( 19,361\,k+53 \right) =[[19,361\,k+53,6859\,{k}^{2}+ 2014\,k+148,130321\,{k}^{3}+57399\,{k}^{2}+8433\,k+413],[3+19\,k,-4\,k, -2-11\,k,1+7\,k]] {\it PISOT} \left( 19,361\,k+55 \right) =[[19,361\,k+55,6859\,{k}^{2}+ 2090\,k+159],[3+19\,k,-1-2\,k,2+13\,k]] {\it PISOT} \left( 19,361\,k+59 \right) =[[19,361\,k+59,6859\,{k}^{2}+ 2242\,k+183],[3+19\,k,2\,k,1+6\,k]] {\it PISOT} \left( 19,361\,k+60 \right) =[[19,361\,k+60,6859\,{k}^{2}+ 2280\,k+189],[4+19\,k,-3-16\,k,1+6\,k]] {\it PISOT} \left( 19,361\,k+61 \right) =[[19,361\,k+61,6859\,{k}^{2}+ 2318\,k+196],[3+19\,k,1+4\,k,-1-6\,k]] {\it PISOT} \left( 19,361\,k+64 \right) =[[19,361\,k+64,6859\,{k}^{2}+ 2432\,k+216],[4+19\,k,-3-12\,k,3+17\,k]] {\it PISOT} \left( 19,361\,k+65 \right) =[[19,361\,k+65],[4+19\,k,-2-11 \,k]] {\it PISOT} \left( 19,361\,k+66 \right) =[[19,361\,k+66,6859\,{k}^{2}+ 2508\,k+229,130321\,{k}^{3}+71478\,{k}^{2}+13058\,k+795],[4+19\,k,-2-10 \,k,3\,k,2+11\,k]] {\it PISOT} \left( 19,361\,k+71 \right) =[[19,361\,k+71],[4+19\,k,-1-5 \,k]] {\it PISOT} \left( 19,361\,k+72 \right) =[[19,361\,k+72],[3+19\,k,3+15 \,k]] {\it PISOT} \left( 19,361\,k+73 \right) =[[19,361\,k+73,6859\,{k}^{2}+ 2774\,k+280,130321\,{k}^{3}+79059\,{k}^{2}+15969\,k+1074,2476099\,{k}^{ 4}+2002828\,{k}^{3}+606993\,{k}^{2}+81692\,k+4120],[4+19\,k,-3\,k,-3-12 \,k,2+11\,k,1+5\,k]] {\it PISOT} \left( 19,361\,k+74 \right) =[[19,361\,k+74,6859\,{k}^{2}+ 2812\,k+288,130321\,{k}^{3}+80142\,{k}^{2}+16420\,k+1121],[4+19\,k,-1-2 \,k,2+11\,k,1+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.972567120206416 {\it PISOT} \left( 19,361\,k+78 \right) =[[19,361\,k+78,6859\,{k}^{2}+ 2964\,k+320,130321\,{k}^{3}+84474\,{k}^{2}+18244\,k+1313],[4+19\,k,2\,k ,1+8\,k,3+14\,k]] {\it PISOT} \left( 19,361\,k+79 \right) =[[19,361\,k+79,6859\,{k}^{2}+ 3002\,k+328],[5+19\,k,-4-16\,k,2+9\,k]] {\it PISOT} \left( 19,361\,k+81 \right) =[[19,361\,k+81,6859\,{k}^{2}+ 3078\,k+345,130321\,{k}^{3}+87723\,{k}^{2}+19671\,k+1469,2476099\,{k}^{ 4}+2222316\,{k}^{3}+747612\,{k}^{2}+111712\,k+6255],[4+19\,k,1+5\,k,1+2 \,k,-2-11\,k,-2-9\,k]] {\it PISOT} \left( 19,361\,k+83 \right) =[[19,361\,k+83,6859\,{k}^{2}+ 3154\,k+363,130321\,{k}^{3}+89889\,{k}^{2}+20683\,k+1588,2476099\,{k}^{ 4}+2277188\,{k}^{3}+785802\,{k}^{2}+120602\,k+6947,47045881\,{k}^{5}+ 54083215\,{k}^{4}+24880842\,{k}^{3}+5726297\,{k}^{2}+659363\,k+30391],[ 4+19\,k,2+7\,k,-2-7\,k,2+8\,k,-3\,k,-3-13\,k]] {\it PISOT} \left( 19,361\,k+84 \right) =[[19,361\,k+84,6859\,{k}^{2}+ 3192\,k+371,130321\,{k}^{3}+90972\,{k}^{2}+21154\,k+1639],[4+19\,k,2+8 \,k,-3\,k,-3-13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.975627999148667 {\it PISOT} \left( 19,361\,k+88 \right) =[[19,361\,k+88,6859\,{k}^{2}+ 3344\,k+408,130321\,{k}^{3}+95304\,{k}^{2}+23248\,k+1892,2476099\,{k}^{ 4}+2414368\,{k}^{3}+883272\,{k}^{2}+143704\,k+8774],[5+19\,k,-2-7\,k,1+ 6\,k,2+9\,k,1+4\,k]] {\it PISOT} \left( 19,361\,k+89 \right) =[[19,361\,k+89,6859\,{k}^{2}+ 3382\,k+417],[4+19\,k,3+13\,k,1+4\,k]] {\it PISOT} \left( 19,361\,k+90 \right) =[[19,361\,k+90,6859\,{k}^{2}+ 3420\,k+426,130321\,{k}^{3}+97470\,{k}^{2}+24288\,k+2016],[4+19\,k,3+14 \,k,2+9\,k,1+4\,k]] {\it PISOT} \left( 19,361\,k+91 \right) =[[19,361\,k+91],[5+19\,k,-1-4 \,k]] {\it PISOT} \left( 19,361\,k+92 \right) =[[19,361\,k+92,6859\,{k}^{2}+ 3496\,k+445],[5+19\,k,-1-3\,k,1+4\,k]] {\it PISOT} \left( 19,361\,k+102 \right) =[[19,361\,k+102],[5+19\,k,2+7 \,k]] {\it PISOT} \left( 19,361\,k+108 \right) =[[19,361\,k+108,6859\,{k}^{2} +4104\,k+614],[7+19\,k,-8-25\,k,3+10\,k]] {\it PISOT} \left( 19,361\,k+109 \right) =[[19,361\,k+109,6859\,{k}^{2} +4142\,k+625],[6+19\,k,-1-5\,k,-3-10\,k]] {\it PISOT} \left( 19,361\,k+111 \right) =[[19,361\,k+111,6859\,{k}^{2} +4218\,k+648,130321\,{k}^{3}+120213\,{k}^{2}+36945\,k+3783],[6+19\,k,-1 -3\,k,1+k,-4-13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998711247926498 {\it PISOT} \left( 19,361\,k+117 \right) =[[19,361\,k+117,6859\,{k}^{2} +4446\,k+720,130321\,{k}^{3}+126711\,{k}^{2}+41049\,k+4431],[6+19\,k,3 \,k,6+18\,k,-1-3\,k]] {\it PISOT} \left( 19,361\,k+119 \right) =[[19,361\,k+119,6859\,{k}^{2} +4522\,k+745,130321\,{k}^{3}+128877\,{k}^{2}+42471\,k+4664],[7+19\,k,-5 -14\,k,2+7\,k,2+6\,k]] {\it PISOT} \left( 19,361\,k+120 \right) =[[19,361\,k+120],[6+19\,k,2+6 \,k]] {\it PISOT} \left( 19,361\,k+121 \right) =[[19,361\,k+121],[7+19\,k,-4- 12\,k]] {\it PISOT} \left( 19,361\,k+122 \right) =[[19,361\,k+122,6859\,{k}^{2} +4636\,k+783,130321\,{k}^{3}+132126\,{k}^{2}+44638\,k+5025],[7+19\,k,-4 -11\,k,2+5\,k,-2-6\,k]] {\it PISOT} \left( 19,361\,k+123 \right) =[[19,361\,k+123,6859\,{k}^{2} +4674\,k+796,130321\,{k}^{3}+133209\,{k}^{2}+45377\,k+5151,2476099\,{k} ^{4}+3374628\,{k}^{3}+1724421\,{k}^{2}+391554\,k+33333,47045881\,{k}^{5 }+80147415\,{k}^{4}+54608470\,{k}^{3}+18600912\,{k}^{2}+3167416\,k+ 215704],[7+19\,k,-3-10\,k,-3-8\,k,2+5\,k,-2-5\,k,2+6\,k]] {\it PISOT} \left( 19,361\,k+124 \right) =[[19,361\,k+124,6859\,{k}^{2} +4712\,k+809,130321\,{k}^{3}+134292\,{k}^{2}+46118\,k+5278],[5+19\,k,9+ 29\,k,6+18\,k,1+3\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.971424913066440 {\it PISOT} \left( 19,361\,k+125 \right) =[[19,361\,k+125,6859\,{k}^{2} +4750\,k+822,130321\,{k}^{3}+135375\,{k}^{2}+46861\,k+5405,2476099\,{k} ^{4}+3429500\,{k}^{3}+1780851\,{k}^{2}+410890\,k+35540,47045881\,{k}^{5 }+81450625\,{k}^{4}+56396142\,{k}^{3}+19520240\,{k}^{2}+3377454\,k+ 233689],[6+19\,k,4+11\,k,-2-4\,k,3+11\,k,5+15\,k,1+3\,k]] {\it PISOT} \left( 19,361\,k+127 \right) =[[19,361\,k+127,6859\,{k}^{2} +4826\,k+849],[7+19\,k,-3-6\,k,6+17\,k]] {\it PISOT} \left( 19,361\,k+132 \right) =[[19,361\,k+132,6859\,{k}^{2} +5016\,k+917],[6+19\,k,6+18\,k,4+11\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.981123249397955 {\it PISOT} \left( 19,361\,k+134 \right) =[[19,361\,k+134,6859\,{k}^{2} +5092\,k+945,130321\,{k}^{3}+145122\,{k}^{2}+53866\,k+6664,2476099\,{k} ^{4}+3676424\,{k}^{3}+2046927\,{k}^{2}+506492\,k+46994,47045881\,{k}^{5 }+87315070\,{k}^{4}+64819716\,{k}^{3}+24059036\,{k}^{2}+4464749\,k+ 331398],[6+19\,k,6+20\,k,9+27\,k,6+19\,k,7+20\,k,3+8\,k]] {\it PISOT} \left( 19,361\,k+139 \right) =[[19,361\,k+139],[8+19\,k,-5- 13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.997367307066144 {\it PISOT} \left( 19,361\,k+140 \right) =[[19,361\,k+140,6859\,{k}^{2} +5320\,k+1032,130321\,{k}^{3}+151620\,{k}^{2}+58816\,k+7607],[7+19\,k,3 +7\,k,-1-5\,k,-7-18\,k]] {\it PISOT} \left( 19,361\,k+144 \right) =[[19,361\,k+144,6859\,{k}^{2} +5472\,k+1091],[8+19\,k,-4-8\,k,6+15\,k]] {\it PISOT} \left( 19,361\,k+146 \right) =[[19,361\,k+146,6859\,{k}^{2} +5548\,k+1122],[7+19\,k,5+13\,k,2+5\,k]] {\it PISOT} \left( 19,361\,k+147 \right) =[[19,361\,k+147,6859\,{k}^{2} +5586\,k+1137,130321\,{k}^{3}+159201\,{k}^{2}+64815\,k+8794],[7+19\,k,5 +14\,k,5+13\,k,2+5\,k]] {\it PISOT} \left( 19,361\,k+151 \right) =[[19,361\,k+151,6859\,{k}^{2} +5738\,k+1200],[9+19\,k,-9-20\,k,5+12\,k]] {\it PISOT} \left( 19,361\,k+154 \right) =[[19,361\,k+154,6859\,{k}^{2} +5852\,k+1248],[9+19\,k,-8-17\,k,6+14\,k]] {\it PISOT} \left( 19,361\,k+155 \right) =[[19,361\,k+155,6859\,{k}^{2} +5890\,k+1264],[8+19\,k,2+3\,k,-6-14\,k]] {\it PISOT} \left( 19,361\,k+159 \right) =[[19,361\,k+159,6859\,{k}^{2} +6042\,k+1331],[7+19\,k,11+26\,k,4+9\,k]] {\it PISOT} \left( 19,361\,k+160 \right) =[[19,361\,k+160,6859\,{k}^{2} +6080\,k+1347],[8+19\,k,4+8\,k,-4-9\,k]] {\it PISOT} \left( 19,361\,k+161 \right) =[[19,361\,k+161],[8+19\,k,4+9 \,k]] {\it PISOT} \left( 19,361\,k+162 \right) =[[19,361\,k+162,6859\,{k}^{2} +6156\,k+1381,130321\,{k}^{3}+175446\,{k}^{2}+78722\,k+11773],[8+19\,k, 5+10\,k,-4-10\,k,-4-9\,k]] {\it PISOT} \left( 19,361\,k+163 \right) =[[19,361\,k+163,6859\,{k}^{2} +6194\,k+1398,130321\,{k}^{3}+176529\,{k}^{2}+79693\,k+11990],[9+19\,k, -3-8\,k,-6-12\,k,5+11\,k]] {\it PISOT} \left( 19,361\,k+164 \right) =[[19,361\,k+164,6859\,{k}^{2} +6232\,k+1416,130321\,{k}^{3}+177612\,{k}^{2}+80704\,k+12226],[10+19\,k ,-13-26\,k,11+23\,k,-5-11\,k]] {\it PISOT} \left( 19,361\,k+166 \right) =[[19,361\,k+166,6859\,{k}^{2} +6308\,k+1450],[9+19\,k,-3-5\,k,6+13\,k]] {\it PISOT} \left( 19,361\,k+174 \right) =[[19,361\,k+174,6859\,{k}^{2} +6612\,k+1593,130321\,{k}^{3}+188442\,{k}^{2}+90810\,k+14584,2476099\,{ k}^{4}+4773864\,{k}^{3}+3450951\,{k}^{2}+1108556\,k+133517],[9+19\,k,2+ 3\,k,-5-11\,k,-3-6\,k,1+2\,k]] {\it PISOT} \left( 19,361\,k+176 \right) =[[19,361\,k+176,6859\,{k}^{2} +6688\,k+1630,130321\,{k}^{3}+190608\,{k}^{2}+92916\,k+15096],[9+19\,k, 2+5\,k,4+8\,k,-1-2\,k]] {\it PISOT} \left( 19,361\,k+177 \right) =[[19,361\,k+177,6859\,{k}^{2} +6726\,k+1649,130321\,{k}^{3}+191691\,{k}^{2}+93991\,k+15363],[10+19\,k ,-7-13\,k,6+12\,k,-1-2\,k]] {\it PISOT} \left( 19,361\,k+180 \right) =[[19,361\,k+180],[10+19\,k,-5 -10\,k]] {\it PISOT} \left( 19,361\,k+181 \right) =[[19,361\,k+181],[9+19\,k,5+ 10\,k]] {\it PISOT} \left( 19,361\,k+184 \right) =[[19,361\,k+184,6859\,{k}^{2} +6992\,k+1782,130321\,{k}^{3}+199272\,{k}^{2}+101572\,k+17258],[9+19\,k ,6+13\,k,6+12\,k,1+2\,k]] {\it PISOT} \left( 19,361\,k+185 \right) =[[19,361\,k+185,6859\,{k}^{2} +7030\,k+1801,130321\,{k}^{3}+200355\,{k}^{2}+102663\,k+17533],[10+19\, k,-3-5\,k,4+8\,k,1+2\,k]] {\it PISOT} \left( 19,361\,k+187 \right) =[[19,361\,k+187,6859\,{k}^{2} +7106\,k+1840,130321\,{k}^{3}+202521\,{k}^{2}+104889\,k+18105,2476099\, {k}^{4}+5130532\,{k}^{3}+3985953\,{k}^{2}+1376150\,k+178147],[10+19\,k, -1-3\,k,-6-11\,k,3+6\,k,1+2\,k]] {\it PISOT} \left( 19,361\,k+195 \right) =[[19,361\,k+195,6859\,{k}^{2} +7410\,k+2001],[10+19\,k,2+5\,k,7+13\,k]] {\it PISOT} \left( 19,361\,k+197 \right) =[[19,361\,k+197,6859\,{k}^{2} +7486\,k+2043,130321\,{k}^{3}+213351\,{k}^{2}+116443\,k+21187],[9+19\,k ,13+26\,k,12+23\,k,6+11\,k]] {\it PISOT} \left( 19,361\,k+198 \right) =[[19,361\,k+198,6859\,{k}^{2} +7524\,k+2063,130321\,{k}^{3}+214434\,{k}^{2}+117598\,k+21495],[10+19\, k,5+8\,k,-6-12\,k,-6-11\,k]] {\it PISOT} \left( 19,361\,k+199 \right) =[[19,361\,k+199,6859\,{k}^{2} +7562\,k+2084,130321\,{k}^{3}+215517\,{k}^{2}+118793\,k+21824],[11+19\, k,-5-10\,k,-6-10\,k,5+9\,k]] {\it PISOT} \left( 19,361\,k+200 \right) =[[19,361\,k+200],[11+19\,k,-5 -9\,k]] {\it PISOT} \left( 19,361\,k+201 \right) =[[19,361\,k+201,6859\,{k}^{2} +7638\,k+2126],[11+19\,k,-4-8\,k,-5-9\,k]] {\it PISOT} \left( 19,361\,k+202 \right) =[[19,361\,k+202,6859\,{k}^{2} +7676\,k+2148],[12+19\,k,-15-26\,k,5+9\,k]] {\it PISOT} \left( 19,361\,k+206 \right) =[[19,361\,k+206,6859\,{k}^{2} +7828\,k+2233],[11+19\,k,-1-3\,k,-8-14\,k]] {\it PISOT} \left( 19,361\,k+207 \right) =[[19,361\,k+207,6859\,{k}^{2} +7866\,k+2255],[10+19\,k,9+17\,k,8+14\,k]] {\it PISOT} \left( 19,361\,k+210 \right) =[[19,361\,k+210,6859\,{k}^{2} +7980\,k+2321],[10+19\,k,11+20\,k,7+12\,k]] {\it PISOT} \left( 19,361\,k+214 \right) =[[19,361\,k+214,6859\,{k}^{2} +8132\,k+2410,130321\,{k}^{3}+231762\,{k}^{2}+137376\,k+27141],[12+19\, k,-9-14\,k,8+13\,k,-3-5\,k]] {\it PISOT} \left( 19,361\,k+215 \right) =[[19,361\,k+215,6859\,{k}^{2} +8170\,k+2433],[12+19\,k,-8-13\,k,3+5\,k]] {\it PISOT} \left( 19,361\,k+217 \right) =[[19,361\,k+217,6859\,{k}^{2} +8246\,k+2478],[11+19\,k,4+8\,k,9+15\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.997366358805359 {\it PISOT} \left( 19,361\,k+221 \right) =[[19,361\,k+221,6859\,{k}^{2} +8398\,k+2571,130321\,{k}^{3}+239343\,{k}^{2}+146539\,k+29910],[12+19\, k,-4-7\,k,-4-5\,k,11+18\,k]] {\it PISOT} \left( 19,361\,k+222 \right) =[[19,361\,k+222],[11+19\,k,8+ 13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.981123544426591 {\it PISOT} \left( 19,361\,k+227 \right) =[[19,361\,k+227,6859\,{k}^{2} +8626\,k+2712,130321\,{k}^{3}+245841\,{k}^{2}+154585\,k+32401,2476099\, {k}^{4}+6227972\,{k}^{3}+5874249\,{k}^{2}+2462486\,k+387104,47045881\,{ k}^{5}+147914335\,{k}^{4}+186018246\,{k}^{3}+116968502\,{k}^{2}+ 36774950\,k+4624842],[13+19\,k,-14-20\,k,18+27\,k,-13-19\,k,13+20\,k,-5 -8\,k]] {\it PISOT} \left( 19,361\,k+229 \right) =[[19,361\,k+229,6859\,{k}^{2} +8702\,k+2760],[13+19\,k,-12-18\,k,7+11\,k]] {\it PISOT} \left( 19,361\,k+234 \right) =[[19,361\,k+234,6859\,{k}^{2} +8892\,k+2882],[12+19\,k,3+6\,k,11+17\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.971426148905127 {\it PISOT} \left( 19,361\,k+236 \right) =[[19,361\,k+236,6859\,{k}^{2} +8968\,k+2931,130321\,{k}^{3}+255588\,{k}^{2}+167074\,k+36402,2476099\, {k}^{4}+6474896\,{k}^{3}+6348945\,{k}^{2}+2766708\,k+452100,47045881\,{ k}^{5}+153778780\,{k}^{4}+201052452\,{k}^{3}+131423246\,{k}^{2}+ 42952305\,k+5614923],[13+19\,k,-7-11\,k,-2-4\,k,-8-11\,k,10+15\,k,-2-3 \,k]] {\it PISOT} \left( 19,361\,k+237 \right) =[[19,361\,k+237,6859\,{k}^{2} +9006\,k+2956,130321\,{k}^{3}+256671\,{k}^{2}+168497\,k+36869],[14+19\, k,-20-29\,k,12+18\,k,-2-3\,k]] {\it PISOT} \left( 19,361\,k+238 \right) =[[19,361\,k+238,6859\,{k}^{2} +9044\,k+2981,130321\,{k}^{3}+257754\,{k}^{2}+169922\,k+37338,2476099\, {k}^{4}+6529768\,{k}^{3}+6457131\,{k}^{2}+2837800\,k+467671,47045881\,{ k}^{5}+155081990\,{k}^{4}+204477620\,{k}^{3}+134798818\,{k}^{2}+ 44430747\,k+5857736],[12+19\,k,7+10\,k,-5-8\,k,-3-5\,k,-3-5\,k,-4-6\,k] ] {\it PISOT} \left( 19,361\,k+239 \right) =[[19,361\,k+239,6859\,{k}^{2} +9082\,k+3006,130321\,{k}^{3}+258837\,{k}^{2}+171349\,k+37808],[12+19\, k,7+11\,k,3+5\,k,4+6\,k]] {\it PISOT} \left( 19,361\,k+240 \right) =[[19,361\,k+240],[12+19\,k,8+ 12\,k]] {\it PISOT} \left( 19,361\,k+241 \right) =[[19,361\,k+241],[13+19\,k,-4 -6\,k]] {\it PISOT} \left( 19,361\,k+242 \right) =[[19,361\,k+242,6859\,{k}^{2} +9196\,k+3082,130321\,{k}^{3}+262086\,{k}^{2}+175680\,k+39251],[12+19\, k,9+14\,k,5+7\,k,-4-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.998710388662175 {\it PISOT} \left( 19,361\,k+244 \right) =[[19,361\,k+244,6859\,{k}^{2} +9272\,k+3133,130321\,{k}^{3}+264252\,{k}^{2}+178590\,k+40228],[13+19\, k,-3-3\,k,12+18\,k,2+3\,k]] {\it PISOT} \left( 19,361\,k+250 \right) =[[19,361\,k+250,6859\,{k}^{2} +9500\,k+3289,130321\,{k}^{3}+270750\,{k}^{2}+187482\,k+43270],[13+19\, k,2+3\,k,k,9+13\,k]] {\it PISOT} \left( 19,361\,k+252 \right) =[[19,361\,k+252,6859\,{k}^{2} +9576\,k+3342],[13+19\,k,4+5\,k,-7-10\,k]] {\it PISOT} \left( 19,361\,k+253 \right) =[[19,361\,k+253,6859\,{k}^{2} +9614\,k+3369],[12+19\,k,17+25\,k,7+10\,k]] {\it PISOT} \left( 19,361\,k+259 \right) =[[19,361\,k+259],[14+19\,k,-5 -7\,k]] {\it PISOT} \left( 19,361\,k+269 \right) =[[19,361\,k+269,6859\,{k}^{2} +10222\,k+3808],[14+19\,k,2+3\,k,3+4\,k]] {\it PISOT} \left( 19,361\,k+270 \right) =[[19,361\,k+270],[14+19\,k,3+ 4\,k]] {\it PISOT} \left( 19,361\,k+271 \right) =[[19,361\,k+271,6859\,{k}^{2} +10298\,k+3865,130321\,{k}^{3}+293493\,{k}^{2}+220311\,k+55123],[15+19 \,k,-11-14\,k,7+9\,k,-3-4\,k]] {\it PISOT} \left( 19,361\,k+272 \right) =[[19,361\,k+272,6859\,{k}^{2} +10336\,k+3894],[15+19\,k,-10-13\,k,3+4\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.975626817576613 {\it PISOT} \left( 19,361\,k+273 \right) =[[19,361\,k+273,6859\,{k}^{2} +10374\,k+3923,130321\,{k}^{3}+295659\,{k}^{2}+223603\,k+56373,2476099 \,{k}^{4}+7490028\,{k}^{3}+8496762\,{k}^{2}+4284132\,k+810073],[14+19\, k,5+7\,k,5+6\,k,-7-9\,k,3+4\,k]] {\it PISOT} \left( 19,361\,k+277 \right) =[[19,361\,k+277,6859\,{k}^{2} +10526\,k+4038,130321\,{k}^{3}+299991\,{k}^{2}+230173\,k+58864],[15+19 \,k,-6-8\,k,-3-3\,k,10+13\,k]] {\it PISOT} \left( 19,361\,k+278 \right) =[[19,361\,k+278,6859\,{k}^{2} +10564\,k+4068,130321\,{k}^{3}+301074\,{k}^{2}+231868\,k+59527,2476099 \,{k}^{4}+7627208\,{k}^{3}+8810832\,{k}^{2}+4523834\,k+871058,47045881 \,{k}^{5}+181146190\,{k}^{4}+279006792\,{k}^{3}+214875749\,{k}^{2}+ 82745840\,k+12746183],[15+19\,k,-5-7\,k,-5-7\,k,-6-8\,k,-3-3\,k,10+13\, k]] {\it PISOT} \left( 19,361\,k+280 \right) =[[19,361\,k+280,6859\,{k}^{2} +10640\,k+4126,130321\,{k}^{3}+303240\,{k}^{2}+235188\,k+60800,2476099 \,{k}^{4}+7682080\,{k}^{3}+8937258\,{k}^{2}+4620960\,k+895938],[15+19\, k,-4-5\,k,1+2\,k,9+11\,k,-7-9\,k]] {\it PISOT} \left( 19,361\,k+282 \right) =[[19,361\,k+282,6859\,{k}^{2} +10716\,k+4185],[14+19\,k,12+16\,k,7+9\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.972567645919480 {\it PISOT} \left( 19,361\,k+283 \right) =[[19,361\,k+283,6859\,{k}^{2} +10754\,k+4215,130321\,{k}^{3}+306489\,{k}^{2}+240259\,k+62778],[15+19 \,k,-2-2\,k,7+8\,k,-11-14\,k]] {\it PISOT} \left( 19,361\,k+287 \right) =[[19,361\,k+287,6859\,{k}^{2} +10906\,k+4335,130321\,{k}^{3}+310821\,{k}^{2}+247099\,k+65478],[15+19 \,k,1+2\,k,9+11\,k,-4-5\,k]] {\it PISOT} \left( 19,361\,k+288 \right) =[[19,361\,k+288,6859\,{k}^{2} +10944\,k+4365,130321\,{k}^{3}+311904\,{k}^{2}+248814\,k+66157,2476099 \,{k}^{4}+7901568\,{k}^{3}+9455103\,{k}^{2}+5028206\,k+1002692],[15+19 \,k,3+3\,k,-9-12\,k,-9-11\,k,4+5\,k]] {\it PISOT} \left( 19,361\,k+289 \right) =[[19,361\,k+289],[16+19\,k,- 12-15\,k]] {\it PISOT} \left( 19,361\,k+290 \right) =[[19,361\,k+290],[15+19\,k,4+ 5\,k]] {\it PISOT} \left( 19,361\,k+295 \right) =[[19,361\,k+295,6859\,{k}^{2} +11210\,k+4580,130321\,{k}^{3}+319485\,{k}^{2}+261065\,k+71106],[15+19 \,k,8+10\,k,3+3\,k,-9-11\,k]] {\it PISOT} \left( 19,361\,k+296 \right) =[[19,361\,k+296],[15+19\,k,9+ 11\,k]] {\it PISOT} \left( 19,361\,k+297 \right) =[[19,361\,k+297,6859\,{k}^{2} +11286\,k+4643],[15+19\,k,9+12\,k,14+17\,k]] {\it PISOT} \left( 19,361\,k+300 \right) =[[19,361\,k+300,6859\,{k}^{2} +11400\,k+4737],[16+19\,k,-3-4\,k,-5-6\,k]] {\it PISOT} \left( 19,361\,k+301 \right) =[[19,361\,k+301,6859\,{k}^{2} +11438\,k+4768],[15+19\,k,13+16\,k,5+6\,k]] {\it PISOT} \left( 19,361\,k+302 \right) =[[19,361\,k+302,6859\,{k}^{2} +11476\,k+4800],[16+19\,k,-2-2\,k,5+6\,k]] {\it PISOT} \left( 19,361\,k+306 \right) =[[19,361\,k+306,6859\,{k}^{2} +11628\,k+4928],[16+19\,k,1+2\,k,11+13\,k]] {\it PISOT} \left( 19,361\,k+308 \right) =[[19,361\,k+308,6859\,{k}^{2} +11704\,k+4993,130321\,{k}^{3}+333564\,{k}^{2}+284598\,k+80942],[16+19 \,k,4+4\,k,-9-11\,k,-6-7\,k]] {\it PISOT} \left( 19,361\,k+309 \right) =[[19,361\,k+309],[17+19\,k,- 12-14\,k]] {\it PISOT} \left( 19,361\,k+313 \right) =[[19,361\,k+313,6859\,{k}^{2} +11894\,k+5156],[16+19\,k,7+9\,k,13+15\,k]] {\it PISOT} \left( 19,361\,k+315 \right) =[[19,361\,k+315],[17+19\,k,-7 -8\,k]] {\it PISOT} \left( 19,361\,k+318 \right) =[[19,361\,k+318,6859\,{k}^{2} +12084\,k+5322,130321\,{k}^{3}+344394\,{k}^{2}+303360\,k+89068,2476099 \,{k}^{4}+8724648\,{k}^{3}+11527794\,{k}^{2}+6769376\,k+1490625, 47045881\,{k}^{5}+207210390\,{k}^{4}+365048976\,{k}^{3}+321551220\,{k}^ {2}+141614682\,k+24946815],[16+19\,k,11+14\,k,21+25\,k,16+19\,k,11+13\, k,7+8\,k]] {\it PISOT} \left( 19,361\,k+320 \right) =[[19,361\,k+320,6859\,{k}^{2} +12160\,k+5389],[18+19\,k,-20-22\,k,8+9\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.977334117747260 {\it PISOT} \left( 19,361\,k+328 \right) =[[19,361\,k+328,6859\,{k}^{2} +12464\,k+5662,130321\,{k}^{3}+355224\,{k}^{2}+322740\,k+97739,2476099 \,{k}^{4}+8999008\,{k}^{3}+12264234\,{k}^{2}+7428354\,k+1687197, 47045881\,{k}^{5}+213726440\,{k}^{4}+388369576\,{k}^{3}+352852393\,{k}^ {2}+160288514\,k+29124850],[18+19\,k,-13-14\,k,5+5\,k,-7-8\,k,-6-6\,k, 10+11\,k]] {\it PISOT} \left( 19,361\,k+333 \right) =[[19,361\,k+333,6859\,{k}^{2} +12654\,k+5836],[18+19\,k,-9-9\,k,12+13\,k]] {\it PISOT} \left( 19,361\,k+334 \right) =[[19,361\,k+334,6859\,{k}^{2} +12692\,k+5871,130321\,{k}^{3}+361722\,{k}^{2}+334654\,k+103200,2476099 \,{k}^{4}+9163624\,{k}^{3}+12716985\,{k}^{2}+7843428\,k+1814042],[17+19 \,k,10+11\,k,3+3\,k,-3-4\,k,-12-13\,k]] {\it PISOT} \left( 19,361\,k+335 \right) =[[19,361\,k+335,6859\,{k}^{2} +12730\,k+5907,130321\,{k}^{3}+362805\,{k}^{2}+336691\,k+104157],[18+19 \,k,-7-7\,k,10+10\,k,-13-14\,k]] {\it PISOT} \left( 19,361\,k+339 \right) =[[19,361\,k+339],[17+19\,k,15 +16\,k]] {\it PISOT} \left( 19,361\,k+340 \right) =[[19,361\,k+340],[17+19\,k,16 +17\,k]] {\it PISOT} \left( 19,361\,k+341 \right) =[[19,361\,k+341],[17+19\,k,17 +18\,k]] {\it PISOT} \left( 19,361\,k+350 \right) =[[19,361\,k+350,6859\,{k}^{2} +13300\,k+6447,130321\,{k}^{3}+379050\,{k}^{2}+367486\,k+118754,2476099 \,{k}^{4}+9602600\,{k}^{3}+13964601\,{k}^{2}+9025552\,k+2187453],[19+19 \,k,-11-11\,k,6+6\,k,-3-3\,k,1+k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.970256405511744 {\it PISOT} \left( 19,361\,k+351 \right) =[[19,361\,k+351,6859\,{k}^{2} +13338\,k+6484,130321\,{k}^{3}+380133\,{k}^{2}+369593\,k+119779,2476099 \,{k}^{4}+9630036\,{k}^{3}+14044629\,{k}^{2}+9103370\,k+2212679],[18+19 \,k,9+9\,k,-5-5\,k,3+3\,k,-1-k]] {\it PISOT} \left( 19,361\,k+352 \right) =[[19,361\,k+352,6859\,{k}^{2} +13376\,k+6521,130321\,{k}^{3}+381216\,{k}^{2}+371702\,k+120805,2476099 \,{k}^{4}+9657472\,{k}^{3}+14124771\,{k}^{2}+9181374\,k+2237977],[19+19 \,k,-9-9\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 19,361\,k+353 \right) =[[19,361\,k+353,6859\,{k}^{2} +13414\,k+6558,130321\,{k}^{3}+382299\,{k}^{2}+373813\,k+121834],[19+19 \,k,-8-8\,k,3+3\,k,-1-k]] {\it PISOT} \left( 19,361\,k+354 \right) =[[19,361\,k+354,6859\,{k}^{2} +13452\,k+6596,130321\,{k}^{3}+383382\,{k}^{2}+375964\,k+122902],[19+19 \,k,-7-7\,k,3+3\,k,-1-k]] {\it PISOT} \left( 19,361\,k+355 \right) =[[19,361\,k+355,6859\,{k}^{2} +13490\,k+6633,130321\,{k}^{3}+384465\,{k}^{2}+378079\,k+123934],[19+19 \,k,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 19,361\,k+356 \right) =[[19,361\,k+356,6859\,{k}^{2} +13528\,k+6670],[19+19\,k,-5-5\,k,1+k]] {\it PISOT} \left( 19,361\,k+357 \right) =[[19,361\,k+357,6859\,{k}^{2} +13566\,k+6708],[19+19\,k,-4-4\,k,1+k]] {\it PISOT} \left( 19,361\,k+358 \right) =[[19,361\,k+358],[19+19\,k,-3 -3\,k]] {\it PISOT} \left( 19,361\,k+359 \right) =[[19,361\,k+359],[19+19\,k,-2 -2\,k]] {\it PISOT} \left( 19,361\,k+360 \right) =[[19,361\,k+360],[19+19\,k,-1 -k]] {\it PISOT} \left( 20,400\,k+1 \right) =[[20,400\,k+1],[20\,k,k]] {\it PISOT} \left( 20,400\,k+2 \right) =[[20,400\,k+2],[20\,k,2\,k]] {\it PISOT} \left( 20,400\,k+3 \right) =[[20,400\,k+3],[20\,k,3\,k]] {\it PISOT} \left( 20,400\,k+4 \right) =[[20,400\,k+4,8000\,{k}^{2}+160 \,k+1],[20\,k,4\,k,k]] {\it PISOT} \left( 20,400\,k+5 \right) =[[20,400\,k+5,8000\,{k}^{2}+200 \,k+1],[20\,k,5\,k,k]] {\it PISOT} \left( 20,400\,k+6 \right) =[[20,400\,k+6,8000\,{k}^{2}+240 \,k+2,160000\,{k}^{3}+7200\,{k}^{2}+116\,k+1],[20\,k,6\,k,2\,k,k]] {\it PISOT} \left( 20,400\,k+7 \right) =[[20,400\,k+7,8000\,{k}^{2}+280 \,k+2,160000\,{k}^{3}+8400\,{k}^{2}+129\,k+1],[20\,k,7\,k,2\,k,k]] {\it PISOT} \left( 20,400\,k+8 \right) =[[20,400\,k+8,8000\,{k}^{2}+320 \,k+3,160000\,{k}^{3}+9600\,{k}^{2}+184\,k+1],[20\,k,8\,k,3\,k,k]] {\it PISOT} \left( 20,400\,k+9 \right) =[[20,400\,k+9,8000\,{k}^{2}+360 \,k+4,160000\,{k}^{3}+10800\,{k}^{2}+241\,k+2,3200000\,{k}^{4}+288000\, {k}^{3}+9660\,{k}^{2}+152\,k+1],[20\,k,9\,k,4\,k,2\,k,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.972801372680209 {\it PISOT} \left( 20,400\,k+10 \right) =[[20,400\,k+10,8000\,{k}^{2}+ 400\,k+5,160000\,{k}^{3}+12000\,{k}^{2}+300\,k+3,3200000\,{k}^{4}+ 320000\,{k}^{3}+12000\,{k}^{2}+220\,k+2,64000000\,{k}^{5}+8000000\,{k}^ {4}+400000\,{k}^{3}+10600\,{k}^{2}+165\,k+1],[1+20\,k,-10\,k,-5\,k,-2\, k,-k,-k]] {\it PISOT} \left( 20,400\,k+11 \right) =[[20,400\,k+11,8000\,{k}^{2}+ 440\,k+6,160000\,{k}^{3}+13200\,{k}^{2}+361\,k+3,3200000\,{k}^{4}+ 352000\,{k}^{3}+14460\,{k}^{2}+252\,k+1],[20\,k,11\,k,6\,k,3\,k,k]] {\it PISOT} \left( 20,400\,k+12 \right) =[[20,400\,k+12,8000\,{k}^{2}+ 480\,k+7,160000\,{k}^{3}+14400\,{k}^{2}+424\,k+4,3200000\,{k}^{4}+ 384000\,{k}^{3}+17040\,{k}^{2}+328\,k+2,64000000\,{k}^{5}+9600000\,{k}^ {4}+569600\,{k}^{3}+16608\,{k}^{2}+225\,k+1],[20\,k,12\,k,7\,k,4\,k,2\, k,k]] {\it PISOT} \left( 20,400\,k+21 \right) =[[20,400\,k+21],[2+20\,k,-1-19 \,k]] {\it PISOT} \left( 20,400\,k+22 \right) =[[20,400\,k+22],[2+20\,k,-1-18 \,k]] {\it PISOT} \left( 20,400\,k+23 \right) =[[20,400\,k+23],[2+20\,k,-1-17 \,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.983851245585674 {\it PISOT} \left( 20,400\,k+27 \right) =[[20,400\,k+27,8000\,{k}^{2}+ 1080\,k+36,160000\,{k}^{3}+32400\,{k}^{2}+2169\,k+48],[1+20\,k,1+7\,k,- 11\,k,-1-15\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.980902997488959 {\it PISOT} \left( 20,400\,k+28 \right) =[[20,400\,k+28,8000\,{k}^{2}+ 1120\,k+39,160000\,{k}^{3}+33600\,{k}^{2}+2344\,k+54,3200000\,{k}^{4}+ 896000\,{k}^{3}+93840\,{k}^{2}+4344\,k+75],[2+20\,k,-1-12\,k,3\,k,1+4\, k,-1-14\,k]] {\it PISOT} \left( 20,400\,k+33 \right) =[[20,400\,k+33,8000\,{k}^{2}+ 1320\,k+54],[2+20\,k,-7\,k,-1-12\,k]] {\it PISOT} \left( 20,400\,k+34 \right) =[[20,400\,k+34,8000\,{k}^{2}+ 1360\,k+58,160000\,{k}^{3}+40800\,{k}^{2}+3476\,k+99,3200000\,{k}^{4}+ 1088000\,{k}^{3}+138960\,{k}^{2}+7904\,k+169],[1+20\,k,1+14\,k,4\,k,7\, k,1+12\,k]] {\it PISOT} \left( 20,400\,k+36 \right) =[[20,400\,k+36,8000\,{k}^{2}+ 1440\,k+65,160000\,{k}^{3}+43200\,{k}^{2}+3896\,k+117,3200000\,{k}^{4}+ 1152000\,{k}^{3}+155760\,{k}^{2}+9360\,k+211,64000000\,{k}^{5}+28800000 \,{k}^{4}+5190400\,{k}^{3}+467856\,{k}^{2}+21089\,k+381],[2+20\,k,-1-4 \,k,1+13\,k,3\,k,6\,k,1+11\,k]] {\it PISOT} \left( 20,400\,k+37 \right) =[[20,400\,k+37,8000\,{k}^{2}+ 1480\,k+68],[1+20\,k,1+17\,k,1+11\,k]] {\it PISOT} \left( 20,400\,k+41 \right) =[[20,400\,k+41,8000\,{k}^{2}+ 1640\,k+84,160000\,{k}^{3}+49200\,{k}^{2}+5041\,k+172,3200000\,{k}^{4}+ 1312000\,{k}^{3}+201660\,{k}^{2}+13768\,k+352],[2+20\,k,-1+k,2+22\,k,5 \,k,1+10\,k]] {\it PISOT} \left( 20,400\,k+44 \right) =[[20,400\,k+44,8000\,{k}^{2}+ 1760\,k+97],[2+20\,k,4\,k,1+9\,k]] {\it PISOT} \left( 20,400\,k+45 \right) =[[20,400\,k+45,8000\,{k}^{2}+ 1800\,k+101],[2+20\,k,1+5\,k,-1-9\,k]] {\it PISOT} \left( 20,400\,k+49 \right) =[[20,400\,k+49,8000\,{k}^{2}+ 1960\,k+120,160000\,{k}^{3}+58800\,{k}^{2}+7201\,k+294],[3+20\,k,-2-11 \,k,2+13\,k,-1-8\,k]] {\it PISOT} \left( 20,400\,k+50 \right) =[[20,400\,k+50,8000\,{k}^{2}+ 2000\,k+125,160000\,{k}^{3}+60000\,{k}^{2}+7500\,k+313],[3+20\,k,-1-10 \,k,-1-5\,k,1+8\,k]] {\it PISOT} \left( 20,400\,k+51 \right) =[[20,400\,k+51,8000\,{k}^{2}+ 2040\,k+130],[2+20\,k,1+11\,k,1+8\,k]] {\it PISOT} \left( 20,400\,k+57 \right) =[[20,400\,k+57,8000\,{k}^{2}+ 2280\,k+162],[4+20\,k,-4-23\,k,2+14\,k]] {\it PISOT} \left( 20,400\,k+61 \right) =[[20,400\,k+61,8000\,{k}^{2}+ 2440\,k+186,160000\,{k}^{3}+73200\,{k}^{2}+11161\,k+567],[4+20\,k,-4-19 \,k,4+22\,k,-2-13\,k]] {\it PISOT} \left( 20,400\,k+66 \right) =[[20,400\,k+66],[3+20\,k,1+6\, k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.989005296549418 {\it PISOT} \left( 20,400\,k+67 \right) =[[20,400\,k+67,8000\,{k}^{2}+ 2680\,k+224,160000\,{k}^{3}+80400\,{k}^{2}+13449\,k+749,3200000\,{k}^{4 }+2144000\,{k}^{3}+538140\,{k}^{2}+59976\,k+2504],[3+20\,k,1+7\,k,1+3\, k,-2-10\,k,1+6\,k]] {\it PISOT} \left( 20,400\,k+68 \right) =[[20,400\,k+68,8000\,{k}^{2}+ 2720\,k+231,160000\,{k}^{3}+81600\,{k}^{2}+13864\,k+785,3200000\,{k}^{4 }+2176000\,{k}^{3}+554640\,{k}^{2}+62816\,k+2668],[3+20\,k,1+8\,k,1+7\, k,1+4\,k,-1-6\,k]] {\it PISOT} \left( 20,400\,k+72 \right) =[[20,400\,k+72,8000\,{k}^{2}+ 2880\,k+259],[4+20\,k,-2-8\,k,2+11\,k]] {\it PISOT} \left( 20,400\,k+75 \right) =[[20,400\,k+75,8000\,{k}^{2}+ 3000\,k+281],[3+20\,k,2+15\,k,3+16\,k]] {\it PISOT} \left( 20,400\,k+77 \right) =[[20,400\,k+77,8000\,{k}^{2}+ 3080\,k+296,160000\,{k}^{3}+92400\,{k}^{2}+17769\,k+1138,3200000\,{k}^{ 4}+2464000\,{k}^{3}+710940\,{k}^{2}+91104\,k+4375],[4+20\,k,-1-3\,k,2+8 \,k,-2-9\,k,1+5\,k]] {\it PISOT} \left( 20,400\,k+78 \right) =[[20,400\,k+78,8000\,{k}^{2}+ 3120\,k+304,160000\,{k}^{3}+93600\,{k}^{2}+18244\,k+1185],[5+20\,k,-5- 22\,k,3+14\,k,-1-5\,k]] {\it PISOT} \left( 20,400\,k+81 \right) =[[20,400\,k+81,8000\,{k}^{2}+ 3240\,k+328],[3+20\,k,4+21\,k,1+5\,k]] {\it PISOT} \left( 20,400\,k+82 \right) =[[20,400\,k+82,8000\,{k}^{2}+ 3280\,k+336,160000\,{k}^{3}+98400\,{k}^{2}+20164\,k+1377],[5+20\,k,-4- 18\,k,1+6\,k,1+5\,k]] {\it PISOT} \left( 20,400\,k+86 \right) =[[20,400\,k+86],[5+20\,k,-3-14 \,k]] {\it PISOT} \left( 20,400\,k+88 \right) =[[20,400\,k+88,8000\,{k}^{2}+ 3520\,k+387,160000\,{k}^{3}+105600\,{k}^{2}+23224\,k+1702],[5+20\,k,-3- 12\,k,2+7\,k,-2-9\,k]] {\it PISOT} \left( 20,400\,k+89 \right) =[[20,400\,k+89],[4+20\,k,2+9\, k]] {\it PISOT} \left( 20,400\,k+93 \right) =[[20,400\,k+93],[4+20\,k,3+13 \,k]] {\it PISOT} \left( 20,400\,k+98 \right) =[[20,400\,k+98,8000\,{k}^{2}+ 3920\,k+480,160000\,{k}^{3}+117600\,{k}^{2}+28804\,k+2351,3200000\,{k}^ {4}+3136000\,{k}^{3}+1152240\,{k}^{2}+188120\,k+11515],[5+20\,k,-1-2\,k ,2+10\,k,2+9\,k,1+4\,k]] {\it PISOT} \left( 20,400\,k+101 \right) =[[20,400\,k+101,8000\,{k}^{2} +4040\,k+510],[6+20\,k,-5-19\,k,1+4\,k]] {\it PISOT} \left( 20,400\,k+102 \right) =[[20,400\,k+102,8000\,{k}^{2} +4080\,k+520,160000\,{k}^{3}+122400\,{k}^{2}+31204\,k+2651,3200000\,{k} ^{4}+3264000\,{k}^{3}+1248240\,{k}^{2}+212120\,k+13515],[5+20\,k,1+2\,k ,-2-10\,k,-3-11\,k,1+4\,k]] {\it PISOT} \left( 20,400\,k+109 \right) =[[20,400\,k+109],[6+20\,k,-3- 11\,k]] {\it PISOT} \left( 20,400\,k+110 \right) =[[20,400\,k+110,8000\,{k}^{2} +4400\,k+605,160000\,{k}^{3}+132000\,{k}^{2}+36300\,k+3328,3200000\,{k} ^{4}+3520000\,{k}^{3}+1452000\,{k}^{2}+266220\,k+18307,64000000\,{k}^{5 }+88000000\,{k}^{4}+48400000\,{k}^{3}+13310600\,{k}^{2}+1830465\,k+ 100705],[5+20\,k,3+10\,k,-1-5\,k,-2-7\,k,2\,k,3+11\,k]] {\it PISOT} \left( 20,400\,k+113 \right) =[[20,400\,k+113],[6+20\,k,-2- 7\,k]] {\it PISOT} \left( 20,400\,k+114 \right) =[[20,400\,k+114],[5+20\,k,4+ 14\,k]] {\it PISOT} \left( 20,400\,k+119 \right) =[[20,400\,k+119,8000\,{k}^{2} +4760\,k+708,160000\,{k}^{3}+142800\,{k}^{2}+42481\,k+4212],[7+20\,k,-6 -21\,k,-2-5\,k,3+10\,k]] {\it PISOT} \left( 20,400\,k+125 \right) =[[20,400\,k+125,8000\,{k}^{2} +5000\,k+781],[5+20\,k,7+25\,k,5+16\,k]] {\it PISOT} \left( 20,400\,k+132 \right) =[[20,400\,k+132,8000\,{k}^{2} +5280\,k+871,160000\,{k}^{3}+158400\,{k}^{2}+52264\,k+5747],[7+20\,k,-3 -8\,k,2+7\,k,2+6\,k]] {\it PISOT} \left( 20,400\,k+133 \right) =[[20,400\,k+133,8000\,{k}^{2} +5320\,k+884],[6+20\,k,4+13\,k,2+6\,k]] {\it PISOT} \left( 20,400\,k+134 \right) =[[20,400\,k+134],[7+20\,k,-2- 6\,k]] {\it PISOT} \left( 20,400\,k+135 \right) =[[20,400\,k+135,8000\,{k}^{2} +5400\,k+911,160000\,{k}^{3}+162000\,{k}^{2}+54665\,k+6148,3200000\,{k} ^{4}+4320000\,{k}^{3}+2186700\,{k}^{2}+491890\,k+41491],[8+20\,k,-9-25 \,k,4+11\,k,-2-5\,k,2+6\,k]] {\it PISOT} \left( 20,400\,k+145 \right) =[[20,400\,k+145,8000\,{k}^{2} +5800\,k+1051],[8+20\,k,-6-15\,k,4+11\,k]] {\it PISOT} \left( 20,400\,k+146 \right) =[[20,400\,k+146,8000\,{k}^{2} +5840\,k+1066,160000\,{k}^{3}+175200\,{k}^{2}+63956\,k+7783],[7+20\,k,2 +6\,k,2+4\,k,-4-11\,k]] {\it PISOT} \left( 20,400\,k+149 \right) =[[20,400\,k+149,8000\,{k}^{2} +5960\,k+1110,160000\,{k}^{3}+178800\,{k}^{2}+66601\,k+8269],[7+20\,k,3 +9\,k,3+7\,k,-3-8\,k]] {\it PISOT} \left( 20,400\,k+150 \right) =[[20,400\,k+150,8000\,{k}^{2} +6000\,k+1125,160000\,{k}^{3}+180000\,{k}^{2}+67500\,k+8438],[8+20\,k,- 3-10\,k,-6-15\,k,3+8\,k]] {\it PISOT} \left( 20,400\,k+151 \right) =[[20,400\,k+151,8000\,{k}^{2} +6040\,k+1140],[8+20\,k,-3-9\,k,-3-8\,k]] {\it PISOT} \left( 20,400\,k+153 \right) =[[20,400\,k+153,8000\,{k}^{2} +6120\,k+1170],[9+20\,k,-11-27\,k,5+13\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.995015191272054 {\it PISOT} \left( 20,400\,k+155 \right) =[[20,400\,k+155,8000\,{k}^{2} +6200\,k+1201,160000\,{k}^{3}+186000\,{k}^{2}+72065\,k+9306],[9+20\,k,- 11-25\,k,11+26\,k,-7-18\,k]] {\it PISOT} \left( 20,400\,k+158 \right) =[[20,400\,k+158,8000\,{k}^{2} +6320\,k+1248,160000\,{k}^{3}+189600\,{k}^{2}+74884\,k+9858,3200000\,{k }^{4}+5056000\,{k}^{3}+2995440\,{k}^{2}+788688\,k+77869],[8+20\,k,-1-2 \,k,1+4\,k,5+12\,k,-2-5\,k]] {\it PISOT} \left( 20,400\,k+159 \right) =[[20,400\,k+159,8000\,{k}^{2} +6360\,k+1264,160000\,{k}^{3}+190800\,{k}^{2}+75841\,k+10048],[8+20\,k, -1-k,5+12\,k,-2-5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.987649171158042 {\it PISOT} \left( 20,400\,k+161 \right) =[[20,400\,k+161,8000\,{k}^{2} +6440\,k+1296,160000\,{k}^{3}+193200\,{k}^{2}+77761\,k+10432,3200000\,{ k}^{4}+5152000\,{k}^{3}+3110460\,{k}^{2}+834592\,k+83971,64000000\,{k}^ {5}+128800000\,{k}^{4}+103682400\,{k}^{3}+41730401\,{k}^{2}+8397560\,k+ 675913],[8+20\,k,k,3+8\,k,2+4\,k,-3-8\,k,-2-5\,k]] {\it PISOT} \left( 20,400\,k+162 \right) =[[20,400\,k+162,8000\,{k}^{2} +6480\,k+1312,160000\,{k}^{3}+194400\,{k}^{2}+78724\,k+10626,3200000\,{ k}^{4}+5184000\,{k}^{3}+3149040\,{k}^{2}+850128\,k+86061],[8+20\,k,1+2 \,k,-2-4\,k,3+8\,k,2+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.9746805881 {\it PISOT} \left( 20,400\,k+168 \right) =[[20,400\,k+168,8000\,{k}^{2} +6720\,k+1411],[9+20\,k,-6-12\,k,8+19\,k]] {\it PISOT} \left( 20,400\,k+171 \right) =[[20,400\,k+171,8000\,{k}^{2} +6840\,k+1462],[8+20\,k,4+11\,k,6+14\,k]] {\it PISOT} \left( 20,400\,k+175 \right) =[[20,400\,k+175,8000\,{k}^{2} +7000\,k+1531],[9+20\,k,-3-5\,k,7+16\,k]] {\it PISOT} \left( 20,400\,k+177 \right) =[[20,400\,k+177,8000\,{k}^{2} +7080\,k+1566,160000\,{k}^{3}+212400\,{k}^{2}+93969\,k+13855],[8+20\,k, 8+17\,k,-4-10\,k,-4-9\,k]] {\it PISOT} \left( 20,400\,k+178 \right) =[[20,400\,k+178],[8+20\,k,8+ 18\,k]] {\it PISOT} \left( 20,400\,k+179 \right) =[[20,400\,k+179,8000\,{k}^{2} +7160\,k+1602,160000\,{k}^{3}+214800\,{k}^{2}+96121\,k+14337],[8+20\,k, 8+19\,k,4+10\,k,4+9\,k]] {\it PISOT} \left( 20,400\,k+181 \right) =[[20,400\,k+181,8000\,{k}^{2} +7240\,k+1638],[9+20\,k,1+k,-5-11\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.994067710148259 {\it PISOT} \left( 20,400\,k+184 \right) =[[20,400\,k+184,8000\,{k}^{2} +7360\,k+1693,160000\,{k}^{3}+220800\,{k}^{2}+101576\,k+15577,3200000\, {k}^{4}+5888000\,{k}^{3}+4062960\,{k}^{2}+1246104\,k+143321,64000000\,{ k}^{5}+147200000\,{k}^{4}+135430400\,{k}^{3}+62303344\,{k}^{2}+14331425 \,k+1318669],[9+20\,k,1+4\,k,8+17\,k,-2-4\,k,2+3\,k,-6-13\,k]] {\it PISOT} \left( 20,400\,k+195 \right) =[[20,400\,k+195,8000\,{k}^{2} +7800\,k+1901,160000\,{k}^{3}+234000\,{k}^{2}+114065\,k+18532],[9+20\,k ,7+15\,k,3+6\,k,-1-2\,k]] {\it PISOT} \left( 20,400\,k+196 \right) =[[20,400\,k+196,8000\,{k}^{2} +7840\,k+1921,160000\,{k}^{3}+235200\,{k}^{2}+115256\,k+18828,3200000\, {k}^{4}+6272000\,{k}^{3}+4610160\,{k}^{2}+1506152\,k+184536],[10+20\,k, -2-4\,k,1+k,-5-10\,k,1+2\,k]] {\it PISOT} \left( 20,400\,k+197 \right) =[[20,400\,k+197,8000\,{k}^{2} +7880\,k+1940,160000\,{k}^{3}+236400\,{k}^{2}+116409\,k+19105],[10+20\, k,-1-3\,k,-5-10\,k,1+2\,k]] {\it PISOT} \left( 20,400\,k+198 \right) =[[20,400\,k+198],[10+20\,k,-1 -2\,k]] {\it PISOT} \left( 20,400\,k+199 \right) =[[20,400\,k+199,8000\,{k}^{2} +7960\,k+1980],[10+20\,k,-1-k,5+10\,k]] {\it PISOT} \left( 20,400\,k+201 \right) =[[20,400\,k+201,8000\,{k}^{2} +8040\,k+2020],[10+20\,k,k,5+10\,k]] {\it PISOT} \left( 20,400\,k+202 \right) =[[20,400\,k+202],[10+20\,k,1+ 2\,k]] {\it PISOT} \left( 20,400\,k+203 \right) =[[20,400\,k+203,8000\,{k}^{2} +8120\,k+2060,160000\,{k}^{3}+243600\,{k}^{2}+123609\,k+20904],[10+20\, k,2+3\,k,-5-10\,k,-1-2\,k]] {\it PISOT} \left( 20,400\,k+204 \right) =[[20,400\,k+204,8000\,{k}^{2} +8160\,k+2081,160000\,{k}^{3}+244800\,{k}^{2}+124856\,k+21228,3200000\, {k}^{4}+6528000\,{k}^{3}+4994160\,{k}^{2}+1698168\,k+216544],[10+20\,k, 2+4\,k,k,5+10\,k,1+2\,k]] {\it PISOT} \left( 20,400\,k+205 \right) =[[20,400\,k+205,8000\,{k}^{2} +8200\,k+2101,160000\,{k}^{3}+246000\,{k}^{2}+126065\,k+21533],[11+20\, k,-8-15\,k,3+6\,k,1+2\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.994067548694371 {\it PISOT} \left( 20,400\,k+216 \right) =[[20,400\,k+216,8000\,{k}^{2} +8640\,k+2333,160000\,{k}^{3}+259200\,{k}^{2}+139976\,k+25199,3200000\, {k}^{4}+6912000\,{k}^{3}+5598960\,{k}^{2}+2015816\,k+272177,64000000\,{ k}^{5}+172800000\,{k}^{4}+186630400\,{k}^{3}+100787856\,{k}^{2}+ 27215937\,k+2939812],[11+20\,k,-3-4\,k,9+17\,k,2+4\,k,1+3\,k,7+13\,k]] {\it PISOT} \left( 20,400\,k+219 \right) =[[20,400\,k+219,8000\,{k}^{2} +8760\,k+2398],[11+20\,k,-k,-6-11\,k]] {\it PISOT} \left( 20,400\,k+221 \right) =[[20,400\,k+221,8000\,{k}^{2} +8840\,k+2442,160000\,{k}^{3}+265200\,{k}^{2}+146521\,k+26984],[12+20\, k,-11-19\,k,6+10\,k,-5-9\,k]] {\it PISOT} \left( 20,400\,k+222 \right) =[[20,400\,k+222],[12+20\,k,- 10-18\,k]] {\it PISOT} \left( 20,400\,k+223 \right) =[[20,400\,k+223,8000\,{k}^{2} +8920\,k+2486,160000\,{k}^{3}+267600\,{k}^{2}+149169\,k+27714],[12+20\, k,-9-17\,k,-6-10\,k,5+9\,k]] {\it PISOT} \left( 20,400\,k+225 \right) =[[20,400\,k+225,8000\,{k}^{2} +9000\,k+2531],[11+20\,k,2+5\,k,9+16\,k]] {\it PISOT} \left( 20,400\,k+229 \right) =[[20,400\,k+229,8000\,{k}^{2} +9160\,k+2622],[12+20\,k,-7-11\,k,8+14\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.9746781157 {\it PISOT} \left( 20,400\,k+232 \right) =[[20,400\,k+232,8000\,{k}^{2} +9280\,k+2691],[11+20\,k,6+12\,k,11+19\,k]] {\it PISOT} \left( 20,400\,k+238 \right) =[[20,400\,k+238,8000\,{k}^{2} +9520\,k+2832,160000\,{k}^{3}+285600\,{k}^{2}+169924\,k+33698,3200000\, {k}^{4}+7616000\,{k}^{3}+6797040\,{k}^{2}+2695952\,k+400973],[12+20\,k, -1-2\,k,-2-4\,k,-5-8\,k,3+5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.987649435817977 {\it PISOT} \left( 20,400\,k+239 \right) =[[20,400\,k+239,8000\,{k}^{2} +9560\,k+2856,160000\,{k}^{3}+286800\,{k}^{2}+171361\,k+34129,3200000\, {k}^{4}+7648000\,{k}^{3}+6854460\,{k}^{2}+2730328\,k+407839,64000000\,{ k}^{5}+191200000\,{k}^{4}+228482400\,{k}^{3}+136516799\,{k}^{2}+ 40783958\,k+4873646],[12+20\,k,-1-k,5+8\,k,-2-4\,k,-5-8\,k,3+5\,k]] {\it PISOT} \left( 20,400\,k+241 \right) =[[20,400\,k+241,8000\,{k}^{2} +9640\,k+2904,160000\,{k}^{3}+289200\,{k}^{2}+174241\,k+34993],[12+20\, k,k,7+12\,k,3+5\,k]] {\it PISOT} \left( 20,400\,k+242 \right) =[[20,400\,k+242,8000\,{k}^{2} +9680\,k+2928,160000\,{k}^{3}+290400\,{k}^{2}+175684\,k+35426,3200000\, {k}^{4}+7744000\,{k}^{3}+7027440\,{k}^{2}+2834192\,k+428621],[12+20\,k, 1+2\,k,3+4\,k,-7-12\,k,-3-5\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.995014267642529 {\it PISOT} \left( 20,400\,k+245 \right) =[[20,400\,k+245,8000\,{k}^{2} +9800\,k+3001,160000\,{k}^{3}+294000\,{k}^{2}+180065\,k+36759],[11+20\, k,14+25\,k,15+26\,k,11+18\,k]] {\it PISOT} \left( 20,400\,k+247 \right) =[[20,400\,k+247,8000\,{k}^{2} +9880\,k+3050],[11+20\,k,16+27\,k,8+13\,k]] {\it PISOT} \left( 20,400\,k+249 \right) =[[20,400\,k+249,8000\,{k}^{2} +9960\,k+3100],[12+20\,k,6+9\,k,-5-8\,k]] {\it PISOT} \left( 20,400\,k+251 \right) =[[20,400\,k+251,8000\,{k}^{2} +10040\,k+3150,160000\,{k}^{3}+301200\,{k}^{2}+189001\,k+39532],[13+20 \,k,-6-9\,k,4+7\,k,5+8\,k]] {\it PISOT} \left( 20,400\,k+254 \right) =[[20,400\,k+254,8000\,{k}^{2} +10160\,k+3226,160000\,{k}^{3}+304800\,{k}^{2}+193556\,k+40973],[13+20 \,k,-4-6\,k,2+4\,k,7+11\,k]] {\it PISOT} \left( 20,400\,k+255 \right) =[[20,400\,k+255,8000\,{k}^{2} +10200\,k+3251],[12+20\,k,9+15\,k,7+11\,k]] {\it PISOT} \left( 20,400\,k+265 \right) =[[20,400\,k+265,8000\,{k}^{2} +10600\,k+3511,160000\,{k}^{3}+318000\,{k}^{2}+210665\,k+46517,3200000 \,{k}^{4}+8480000\,{k}^{3}+8426700\,{k}^{2}+3721510\,k+616301],[12+20\, k,16+25\,k,7+11\,k,3+5\,k,4+6\,k]] {\it PISOT} \left( 20,400\,k+266 \right) =[[20,400\,k+266],[13+20\,k,4+ 6\,k]] {\it PISOT} \left( 20,400\,k+267 \right) =[[20,400\,k+267,8000\,{k}^{2} +10680\,k+3564],[14+20\,k,-9-13\,k,4+6\,k]] {\it PISOT} \left( 20,400\,k+268 \right) =[[20,400\,k+268,8000\,{k}^{2} +10720\,k+3591,160000\,{k}^{3}+321600\,{k}^{2}+215464\,k+48117],[13+20 \,k,5+8\,k,5+7\,k,-4-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.999015314865883 {\it PISOT} \left( 20,400\,k+270 \right) =[[20,400\,k+270,8000\,{k}^{2} +10800\,k+3645,160000\,{k}^{3}+324000\,{k}^{2}+218700\,k+49208],[15+20 \,k,-21-30\,k,10+15\,k,2+3\,k]] {\it PISOT} \left( 20,400\,k+275 \right) =[[20,400\,k+275,8000\,{k}^{2} +11000\,k+3781],[15+20\,k,-18-25\,k,11+16\,k]] {\it PISOT} \left( 20,400\,k+281 \right) =[[20,400\,k+281,8000\,{k}^{2} +11240\,k+3948,160000\,{k}^{3}+337200\,{k}^{2}+236881\,k+55469],[13+20 \,k,15+21\,k,-3-5\,k,-7-10\,k]] {\it PISOT} \left( 20,400\,k+286 \right) =[[20,400\,k+286],[15+20\,k,- 10-14\,k]] {\it PISOT} \left( 20,400\,k+287 \right) =[[20,400\,k+287],[14+20\,k,5+ 7\,k]] {\it PISOT} \left( 20,400\,k+290 \right) =[[20,400\,k+290,8000\,{k}^{2} +11600\,k+4205,160000\,{k}^{3}+348000\,{k}^{2}+252300\,k+60973,3200000 \,{k}^{4}+9280000\,{k}^{3}+10092000\,{k}^{2}+4877820\,k+884116],[15+20 \,k,-8-10\,k,11+15\,k,-2-2\,k,8+11\,k]] {\it PISOT} \left( 20,400\,k+291 \right) =[[20,400\,k+291],[14+20\,k,8+ 11\,k]] {\it PISOT} \left( 20,400\,k+298 \right) =[[20,400\,k+298,8000\,{k}^{2} +11920\,k+4440,160000\,{k}^{3}+357600\,{k}^{2}+266404\,k+66153,3200000 \,{k}^{4}+9536000\,{k}^{3}+10656240\,{k}^{2}+5292360\,k+985635],[15+20 \,k,-1-2\,k,-8-10\,k,8+11\,k,3+4\,k]] {\it PISOT} \left( 20,400\,k+299 \right) =[[20,400\,k+299,8000\,{k}^{2} +11960\,k+4470],[14+20\,k,14+19\,k,3+4\,k]] {\it PISOT} \left( 20,400\,k+302 \right) =[[20,400\,k+302,8000\,{k}^{2} +12080\,k+4560,160000\,{k}^{3}+362400\,{k}^{2}+273604\,k+68853,3200000 \,{k}^{4}+9664000\,{k}^{3}+10944240\,{k}^{2}+5508360\,k+1039635],[15+20 \,k,1+2\,k,8+10\,k,-7-9\,k,3+4\,k]] {\it PISOT} \left( 20,400\,k+307 \right) =[[20,400\,k+307],[16+20\,k,- 10-13\,k]] {\it PISOT} \left( 20,400\,k+310 \right) =[[20,400\,k+310,8000\,{k}^{2} +12400\,k+4805,160000\,{k}^{3}+372000\,{k}^{2}+288300\,k+74478,3200000 \,{k}^{4}+9920000\,{k}^{3}+11532000\,{k}^{2}+5958220\,k+1154417],[16+20 \,k,-8-10\,k,4+5\,k,-2-2\,k,7+9\,k]] {\it PISOT} \left( 20,400\,k+311 \right) =[[20,400\,k+311],[16+20\,k,-7 -9\,k]] {\it PISOT} \left( 20,400\,k+312 \right) =[[20,400\,k+312,8000\,{k}^{2} +12480\,k+4867,160000\,{k}^{3}+374400\,{k}^{2}+292024\,k+75922],[15+20 \,k,9+12\,k,5+7\,k,7+9\,k]] {\it PISOT} \left( 20,400\,k+314 \right) =[[20,400\,k+314],[15+20\,k,11 +14\,k]] {\it PISOT} \left( 20,400\,k+318 \right) =[[20,400\,k+318,8000\,{k}^{2} +12720\,k+5056,160000\,{k}^{3}+381600\,{k}^{2}+303364\,k+80387],[15+20 \,k,14+18\,k,5+6\,k,-4-5\,k]] {\it PISOT} \left( 20,400\,k+319 \right) =[[20,400\,k+319,8000\,{k}^{2} +12760\,k+5088],[17+20\,k,-17-21\,k,4+5\,k]] {\it PISOT} \left( 20,400\,k+322 \right) =[[20,400\,k+322,8000\,{k}^{2} +12880\,k+5184,160000\,{k}^{3}+386400\,{k}^{2}+311044\,k+83459],[15+20 \,k,17+22\,k,11+14\,k,4+5\,k]] {\it PISOT} \left( 20,400\,k+323 \right) =[[20,400\,k+323,8000\,{k}^{2} +12920\,k+5216,160000\,{k}^{3}+387600\,{k}^{2}+312969\,k+84231,3200000 \,{k}^{4}+10336000\,{k}^{3}+12518940\,{k}^{2}+6738776\,k+1360211],[16+ 20\,k,2+3\,k,6+8\,k,7+9\,k,4+5\,k]] {\it PISOT} \left( 20,400\,k+325 \right) =[[20,400\,k+325,8000\,{k}^{2} +13000\,k+5281],[17+20\,k,-13-15\,k,13+16\,k]] {\it PISOT} \left( 20,400\,k+328 \right) =[[20,400\,k+328,8000\,{k}^{2} +13120\,k+5379],[16+20\,k,6+8\,k,9+11\,k]] {\it PISOT} \left( 20,400\,k+332 \right) =[[20,400\,k+332,8000\,{k}^{2} +13280\,k+5511,160000\,{k}^{3}+398400\,{k}^{2}+330664\,k+91479,3200000 \,{k}^{4}+10624000\,{k}^{3}+13226640\,{k}^{2}+7318464\,k+1518492],[17+ 20\,k,-7-8\,k,6+7\,k,-3-4\,k,-5-6\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.989005090299476 {\it PISOT} \left( 20,400\,k+333 \right) =[[20,400\,k+333,8000\,{k}^{2} +13320\,k+5544,160000\,{k}^{3}+399600\,{k}^{2}+332649\,k+92300,3200000 \,{k}^{4}+10656000\,{k}^{3}+13306140\,{k}^{2}+7384304\,k+1536668],[17+ 20\,k,-6-7\,k,2+3\,k,8+10\,k,5+6\,k]] {\it PISOT} \left( 20,400\,k+334 \right) =[[20,400\,k+334],[17+20\,k,-5 -6\,k]] {\it PISOT} \left( 20,400\,k+339 \right) =[[20,400\,k+339,8000\,{k}^{2} +13560\,k+5746,160000\,{k}^{3}+406800\,{k}^{2}+344761\,k+97394],[16+20 \,k,15+19\,k,18+22\,k,11+13\,k]] {\it PISOT} \left( 20,400\,k+343 \right) =[[20,400\,k+343,8000\,{k}^{2} +13720\,k+5882],[16+20\,k,19+23\,k,12+14\,k]] {\it PISOT} \left( 20,400\,k+349 \right) =[[20,400\,k+349,8000\,{k}^{2} +13960\,k+6090],[18+20\,k,-10-11\,k,7+8\,k]] {\it PISOT} \left( 20,400\,k+350 \right) =[[20,400\,k+350,8000\,{k}^{2} +14000\,k+6125,160000\,{k}^{3}+420000\,{k}^{2}+367500\,k+107188],[18+20 \,k,-9-10\,k,4+5\,k,7+8\,k]] {\it PISOT} \left( 20,400\,k+351 \right) =[[20,400\,k+351,8000\,{k}^{2} +14040\,k+6160,160000\,{k}^{3}+421200\,{k}^{2}+369601\,k+108107],[17+20 \,k,9+11\,k,11+13\,k,7+8\,k]] {\it PISOT} \left( 20,400\,k+355 \right) =[[20,400\,k+355,8000\,{k}^{2} +14200\,k+6301],[18+20\,k,-4-5\,k,-8-9\,k]] {\it PISOT} \left( 20,400\,k+356 \right) =[[20,400\,k+356,8000\,{k}^{2} +14240\,k+6337],[18+20\,k,-4-4\,k,8+9\,k]] {\it PISOT} \left( 20,400\,k+359 \right) =[[20,400\,k+359,8000\,{k}^{2} +14360\,k+6444,160000\,{k}^{3}+430800\,{k}^{2}+386641\,k+115669,3200000 \,{k}^{4}+11488000\,{k}^{3}+15465660\,{k}^{2}+9253552\,k+2076244],[18+ 20\,k,-2-k,20+22\,k,-5-5\,k,9+10\,k]] {\it PISOT} \left( 20,400\,k+363 \right) =[[20,400\,k+363,8000\,{k}^{2} +14520\,k+6588],[19+20\,k,-16-17\,k,10+11\,k]] {\it PISOT} \left( 20,400\,k+364 \right) =[[20,400\,k+364,8000\,{k}^{2} +14560\,k+6625,160000\,{k}^{3}+436800\,{k}^{2}+397496\,k+120579,3200000 \,{k}^{4}+11648000\,{k}^{3}+15899760\,{k}^{2}+9646160\,k+2194611, 64000000\,{k}^{5}+291200000\,{k}^{4}+529990400\,{k}^{3}+482303344\,{k}^ {2}+219456577\,k+39943252],[18+20\,k,3+4\,k,12+13\,k,-3-3\,k,6+6\,k,-10 -11\,k]] {\it PISOT} \left( 20,400\,k+366 \right) =[[20,400\,k+366,8000\,{k}^{2} +14640\,k+6698,160000\,{k}^{3}+439200\,{k}^{2}+401876\,k+122577,3200000 \,{k}^{4}+11712000\,{k}^{3}+16074960\,{k}^{2}+9806016\,k+2243225],[19+ 20\,k,-13-14\,k,4+4\,k,-7-7\,k,11+12\,k]] {\it PISOT} \left( 20,400\,k+367 \right) =[[20,400\,k+367,8000\,{k}^{2} +14680\,k+6734],[18+20\,k,7+7\,k,-11-12\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.980902231713918 {\it PISOT} \left( 20,400\,k+372 \right) =[[20,400\,k+372,8000\,{k}^{2} +14880\,k+6919,160000\,{k}^{3}+446400\,{k}^{2}+415144\,k+128690,3200000 \,{k}^{4}+11904000\,{k}^{3}+16605840\,{k}^{2}+10295336\,k+2393571],[18+ 20\,k,11+12\,k,3+3\,k,-3-4\,k,-13-14\,k]] Take it with a grain of salt, for k=1000 the Pisot index is, 0.983850698362542 {\it PISOT} \left( 20,400\,k+373 \right) =[[20,400\,k+373,8000\,{k}^{2} +14920\,k+6956,160000\,{k}^{3}+447600\,{k}^{2}+417369\,k+129721],[19+20 \,k,-6-7\,k,-11-11\,k,14+15\,k]] {\it PISOT} \left( 20,400\,k+377 \right) =[[20,400\,k+377],[18+20\,k,16 +17\,k]] {\it PISOT} \left( 20,400\,k+378 \right) =[[20,400\,k+378],[18+20\,k,17 +18\,k]] {\it PISOT} \left( 20,400\,k+379 \right) =[[20,400\,k+379],[18+20\,k,18 +19\,k]] {\it PISOT} \left( 20,400\,k+388 \right) =[[20,400\,k+388,8000\,{k}^{2} +15520\,k+7527,160000\,{k}^{3}+465600\,{k}^{2}+451624\,k+146020,3200000 \,{k}^{4}+12416000\,{k}^{3}+18065040\,{k}^{2}+11681752\,k+2832714, 64000000\,{k}^{5}+310400000\,{k}^{4}+602169600\,{k}^{3}+584092192\,{k}^ {2}+283275809\,k+54953216],[20+20\,k,-12-12\,k,7+7\,k,-4-4\,k,2+2\,k,-1 -k]] {\it PISOT} \left( 20,400\,k+389 \right) =[[20,400\,k+389,8000\,{k}^{2} +15560\,k+7566,160000\,{k}^{3}+466800\,{k}^{2}+453961\,k+147158,3200000 \,{k}^{4}+12448000\,{k}^{3}+18158460\,{k}^{2}+11772668\,k+2862209],[20+ 20\,k,-11-11\,k,6+6\,k,-3-3\,k,1+k]] {\it PISOT} \left( 20,400\,k+390 \right) =[[20,400\,k+390,8000\,{k}^{2} +15600\,k+7605,160000\,{k}^{3}+468000\,{k}^{2}+456300\,k+148298,3200000 \,{k}^{4}+12480000\,{k}^{3}+18252000\,{k}^{2}+11863820\,k+2891821],[20+ 20\,k,-10-10\,k,5+5\,k,-2-2\,k,1+k]] {\it PISOT} \left( 20,400\,k+391 \right) =[[20,400\,k+391,8000\,{k}^{2} +15640\,k+7644,160000\,{k}^{3}+469200\,{k}^{2}+458641\,k+149439,3200000 \,{k}^{4}+12512000\,{k}^{3}+18345660\,{k}^{2}+11955168\,k+2921509],[20+ 20\,k,-9-9\,k,4+4\,k,-2-2\,k,1+k]] {\it PISOT} \left( 20,400\,k+392 \right) =[[20,400\,k+392,8000\,{k}^{2} +15680\,k+7683,160000\,{k}^{3}+470400\,{k}^{2}+460984\,k+150583],[20+20 \,k,-8-8\,k,3+3\,k,-1-k]] {\it PISOT} \left( 20,400\,k+393 \right) =[[20,400\,k+393,8000\,{k}^{2} +15720\,k+7722,160000\,{k}^{3}+471600\,{k}^{2}+463329\,k+151728],[20+20 \,k,-7-7\,k,2+2\,k,-1-k]] {\it PISOT} \left( 20,400\,k+394 \right) =[[20,400\,k+394,8000\,{k}^{2} +15760\,k+7762,160000\,{k}^{3}+472800\,{k}^{2}+465716\,k+152915],[20+20 \,k,-6-6\,k,2+2\,k,-1-k]] {\it PISOT} \left( 20,400\,k+395 \right) =[[20,400\,k+395,8000\,{k}^{2} +15800\,k+7801],[20+20\,k,-5-5\,k,1+k]] {\it PISOT} \left( 20,400\,k+396 \right) =[[20,400\,k+396,8000\,{k}^{2} +15840\,k+7841],[20+20\,k,-4-4\,k,1+k]] {\it PISOT} \left( 20,400\,k+397 \right) =[[20,400\,k+397],[20+20\,k,-3 -3\,k]] {\it PISOT} \left( 20,400\,k+398 \right) =[[20,400\,k+398],[20+20\,k,-2 -2\,k]] {\it PISOT} \left( 20,400\,k+399 \right) =[[20,400\,k+399],[20+20\,k,-1 -k]] 2 The following pairs [a,b], PISOT(a, a k + b, 1/2), do not posses recurrences of order<=, 6 {[4, 3], [4, 6], [4, 13], [5, 4], [5, 7], [5, 18], [5, 21], [6, 5], [6, 9], [6, 10], [6, 16], [6, 21], [6, 26], [6, 27], [6, 31], [7, 5], [7, 6], [7, 10], [7, 11], [7, 38], [7, 39], [7, 43], [7, 44], [8, 6], [8, 7], [8, 10], [8, 12], [8, 14], [8, 19], [8, 29], [8, 30], [8, 34], [8, 35], [8, 45], [8, 50], [8, 52], [8, 54], [8, 57], [8, 58], [9, 7], [9, 8], [9, 14], [9, 15], [9, 19], [9, 22], [9, 23], [9, 24], [9, 30], [9, 33], [9, 34], [9, 35], [9, 37], [9, 44], [9, 46], [9, 47], [9, 48], [9, 51], [9, 57], [9, 58], [9, 59], [9, 62], [9, 66], [9, 67], [9, 73], [9, 74], [10, 6], [10, 7], [10, 8], [10, 9], [10, 13], [10, 14], [10, 15], [10, 17], [10, 18], [10, 19], [10, 21], [10, 22], [10, 23], [10, 27], [10, 28], [10, 31], [10, 36], [10, 37], [10, 42], [10, 44], [10, 46], [10, 47], [10, 53], [10, 54], [10, 56], [10, 58], [10, 63], [10, 64], [10, 69], [10, 72], [10, 73], [10, 77], [10, 78], [10, 79], [10, 82], [10, 83], [10, 85], [10, 86], [10, 87], [10, 91], [10, 92], [10, 93], [11, 8], [11, 9], [11, 10], [11, 14], [11, 16], [11, 17], [11, 21], [11, 26], [11, 27], [11, 28], [11, 31], [11, 32], [11, 34], [11, 35], [11, 37], [11, 38], [11, 43], [11, 45], [11, 47], [11, 52], [11, 54], [11, 56], [11, 58], [11, 59], [11, 62], [11, 63], [11, 65], [11, 67], [11, 69], [11, 74], [11, 76], [11, 78], [11, 83], [11, 84], [11, 86], [11, 87], [11, 89], [11, 90], [11, 93], [11, 94], [11, 95], [11, 100], [11, 104], [11, 105], [11, 107], [11, 111], [11, 112], [11, 113], [12, 9], [12, 10], [12, 11], [12, 15], [12, 17], [12, 18], [12, 19], [12, 22], [12, 25], [12, 26], [12, 27], [12, 31], [12, 33], [12, 35], [12, 39], [12, 40], [12, 43], [12, 44], [12, 45], [12, 46], [12, 47], [12, 50], [12, 51], [12, 52], [12, 53], [12, 54], [12, 55], [12, 56], [12, 57], [12, 62], [12, 63], [12, 65], [12, 66], [12, 67], [12, 69], [12, 75], [12, 77], [12, 78], [12, 79], [12, 81], [12, 82], [12, 87], [12, 88], [12, 89], [12, 91], [12, 92], [12, 93], [12, 94], [12, 97], [12, 98], [12, 99], [12, 100], [12, 101], [12, 104], [12, 105], [12, 109], [12, 111], [12, 113], [12, 117], [12, 118], [12, 119], [12, 122], [12, 125], [12, 127], [12, 129], [12, 133], [12, 134], [12, 135], [13, 9], [13, 10], [13, 11], [13, 12], [13, 16], [13, 17], [13, 18], [13, 20], [13, 25], [13, 27], [13, 30], [13, 31], [13, 36], [13, 40], [13, 42], [13, 45], [13, 47], [13, 49], [13, 50], [13, 53], [13, 54], [13, 60], [13, 62], [13, 63], [13, 67], [13, 70], [13, 73], [13, 74], [13, 76], [13, 77], [13, 79], [13, 80], [13, 81], [13, 88], [13, 89], [13, 90], [13, 92], [13, 93], [13, 95], [13, 96], [13, 99], [13, 102], [13, 106], [13, 107], [13, 109], [13, 115], [13, 116], [13, 119], [13, 120], [13, 122], [13, 124], [13, 127], [13, 129], [13, 133], [13, 138], [13, 139], [13, 142], [13, 144], [13, 149], [13, 151], [13, 152], [13, 153], [13, 157], [13, 158], [13, 159], [13, 160], [14, 9], [14, 10], [14, 11], [14, 12], [14, 13], [14, 17], [14, 18], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 30], [14, 32], [14, 34], [14, 36], [14, 37], [14, 41], [14, 46], [14, 52], [14, 54], [14, 55], [14, 57], [14, 58], [14, 61], [14, 62], [14, 64], [14, 69], [14, 72], [14, 73], [14, 74], [14, 76], [14, 80], [14, 81], [14, 86], [14, 89], [14, 90], [14, 91], [14, 92], [14, 93], [14, 94], [14, 95], [14, 101], [14, 102], [14, 103], [14, 104], [14, 105], [14, 106], [14, 107], [14, 110], [14, 115], [14, 116], [14, 120], [14, 122], [14, 123], [14, 124], [14, 127], [14, 132], [14, 134], [14, 135], [14, 138], [14, 139], [14, 141], [14, 142], [14, 144], [14, 150], [14, 155], [14, 159], [14, 160], [14, 162], [14, 164], [14, 166], [14, 169], [14, 170], [14, 171], [14, 172], [14, 173], [14, 174], [14, 175], [14, 176], [14, 178], [14, 179], [14, 183], [14, 184], [14, 185], [14, 186], [14, 187], [15, 10], [15, 11], [15, 12], [15, 13], [15, 14], [15, 18], [15, 19], [15, 23], [15, 24], [15, 25], [15, 26], [15, 27], [15, 34], [15, 35], [15, 36], [15, 37], [15, 39], [15, 40], [15, 42], [15, 43], [15, 46], [15, 47], [15, 48], [15, 49], [15, 50], [15, 51], [15, 52], [15, 53], [15, 59], [15, 62], [15, 63], [15, 66], [15, 67], [15, 68], [15, 69], [15, 70], [15, 71], [15, 77], [15, 79], [15, 80], [15, 81], [15, 83], [15, 86], [15, 88], [15, 89], [15, 92], [15, 93], [15, 94], [15, 100], [15, 101], [15, 103], [15, 104], [15, 106], [15, 107], [15, 108], [15, 110], [15, 111], [15, 114], [15, 115], [15, 117], [15, 118], [15, 119], [15, 121], [15, 122], [15, 124], [15, 125], [15, 131], [15, 132], [15, 133], [15, 136], [15, 137], [15, 139], [15, 142], [15, 144], [15, 145], [15, 146], [15, 148], [15, 154], [15, 155], [15, 156], [15, 157], [15, 158], [15, 159], [15, 162], [15, 163], [15, 166], [15, 171], [15, 172], [15, 173], [15, 174], [15, 175], [15, 176], [15, 177], [15, 178], [15, 179], [15, 182], [15, 183], [15, 185], [15, 186], [15, 188], [15, 189], [15, 190], [15, 191], [15, 198], [15, 199], [15, 200], [15, 201], [15, 202], [15, 206], [15, 207], [15, 211], [15, 212], [15, 213], [15, 214], [15, 215], [16, 10], [16, 11], [16, 12], [16, 13], [16, 14], [16, 15], [16, 19], [16, 20], [16, 22], [16, 23], [16, 24], [16, 27], [16, 29], [16, 30], [16, 34], [16, 38], [16, 39], [16, 40], [16, 41], [16, 43], [16, 45], [16, 46], [16, 47], [16, 49], [16, 50], [16, 52], [16, 53], [16, 54], [16, 55], [16, 59], [16, 60], [16, 61], [16, 67], [16, 68], [16, 71], [16, 75], [16, 76], [16, 78], [16, 79], [16, 81], [16, 88], [16, 89], [16, 90], [16, 91], [16, 92], [16, 93], [16, 94], [16, 98], [16, 100], [16, 103], [16, 104], [16, 105], [16, 106], [16, 107], [16, 108], [16, 109], [16, 114], [16, 115], [16, 116], [16, 118], [16, 119], [16, 120], [16, 121], [16, 122], [16, 123], [16, 125], [16, 131], [16, 133], [16, 134], [16, 135], [16, 136], [16, 137], [16, 138], [16, 140], [16, 141], [16, 142], [16, 147], [16, 148], [16, 149], [16, 150], [16, 151], [16, 152], [16, 153], [16, 156], [16, 158], [16, 162], [16, 163], [16, 164], [16, 165], [16, 166], [16, 167], [16, 168], [16, 175], [16, 177], [16, 178], [16, 180], [16, 181], [16, 185], [16, 188], [16, 189], [16, 195], [16, 196], [16, 197], [16, 200], [16, 201], [16, 202], [16, 203], [16, 204], [16, 206], [16, 207], [16, 209], [16, 210], [16, 211], [16, 213], [16, 215], [16, 216], [16, 217], [16, 218], [16, 222], [16, 226], [16, 227], [16, 229], [16, 232], [16, 233], [16, 234], [16, 236], [16, 237], [16, 241], [16, 242], [16, 243], [16, 244], [16, 245], [16, 246], [17, 10], [17, 12], [17, 13], [17, 14], [17, 15], [17, 16], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 33], [17, 35], [17, 37], [17, 38], [17, 39], [17, 42], [17, 43], [17, 46], [17, 50], [17, 52], [17, 54], [17, 55], [17, 56], [17, 59], [17, 60], [17, 61], [17, 62], [17, 63], [17, 66], [17, 69], [17, 70], [17, 76], [17, 78], [17, 80], [17, 81], [17, 84], [17, 86], [17, 88], [17, 90], [17, 91], [17, 92], [17, 93], [17, 94], [17, 101], [17, 103], [17, 104], [17, 105], [17, 106], [17, 107], [17, 110], [17, 111], [17, 112], [17, 113], [17, 116], [17, 118], [17, 120], [17, 121], [17, 122], [17, 125], [17, 127], [17, 129], [17, 130], [17, 131], [17, 133], [17, 134], [17, 135], [17, 137], [17, 138], [17, 140], [17, 149], [17, 151], [17, 152], [17, 154], [17, 155], [17, 156], [17, 158], [17, 159], [17, 160], [17, 162], [17, 164], [17, 167], [17, 168], [17, 169], [17, 171], [17, 173], [17, 176], [17, 177], [17, 178], [17, 179], [17, 182], [17, 183], [17, 184], [17, 185], [17, 186], [17, 188], [17, 195], [17, 196], [17, 197], [17, 198], [17, 199], [17, 201], [17, 203], [17, 205], [17, 208], [17, 209], [17, 211], [17, 213], [17, 219], [17, 220], [17, 223], [17, 226], [17, 227], [17, 228], [17, 229], [17, 230], [17, 233], [17, 234], [17, 235], [17, 237], [17, 239], [17, 243], [17, 246], [17, 247], [17, 250], [17, 251], [17, 252], [17, 254], [17, 256], [17, 260], [17, 261], [17, 262], [17, 263], [17, 264], [17, 265], [17, 266], [17, 267], [17, 268], [17, 269], [17, 273], [17, 274], [17, 275], [17, 276], [17, 277], [17, 279], [18, 10], [18, 12], [18, 13], [18, 14], [18, 15], [18, 16], [18, 17], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 30], [18, 31], [18, 32], [18, 33], [18, 34], [18, 35], [18, 37], [18, 38], [18, 40], [18, 42], [18, 43], [18, 44], [18, 45], [18, 48], [18, 49], [18, 50], [18, 51], [18, 52], [18, 53], [18, 56], [18, 57], [18, 58], [18, 60], [18, 61], [18, 62], [18, 63], [18, 66], [18, 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This ends this fascinating article that took, 2901.390, to generated.