read(`code.txt`): Help_tests:=proc() print(` NoPrefixTest(cap) , NoPrefixPrimTest(cap) `): print(` PrefixBySizeTest(cap) , PrefixBySizePrimTest(cap) `): print(` PrefixBySizeNonContTest(cap) `): print(` PrefixBySizeRelPrimeTest(cap) , BySizePrimTest(cap) `): print(` BySizeNoContTest(cap) `): end: #When running for real, set cap to 19 NoPrefixTest:=proc(cap) local filter,stopcond,i: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i) AndFilters(stopcond(i), MakeAtMostTPrefixFilter(0)): end: OpenDB("data.txt"): ResetDB("data.txt"): return seq([ParallelCountAverageFileNoReset("data.txt", [filter(i)],[filter(i)],[LSelector],stopcond(i))],i=1..cap): end: ##DATA #Count sequence: 1, 2, 4, 8, 16, 32, 63, 124, 246, 483, 934, 1825, #3555, 6837, 13604, 25876, 50247, 96900, 188489 #Average sequence: 2., 3.500000000, 4.250000000, 5.875000000, 6.187500000, 8.218750000, 8.714285714, 10.44354839, 11.28861789, 12.95652174, 13.72376874, 15.51123288, 16.16090014, 17.89717712, 19.11945016, 20.56581388, 21.36441977, 23.02528380, 23.89802057 NoPrefixPrimTest:=proc(cap) local filter,stopcond,i: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i) AndFilters(stopcond(i), MakeAtMostTPrefixFilter(0)): end: OpenDB("dataprim.txt"): ResetDB("dataprim.txt"): return seq([ParallelCountAverageFileNoReset("dataprim.txt", [filter(i)],[filter(i)],[LSelector],stopcond(i))],i=1..cap): end: ##DATA #Count sequence: 1, 1, 2, 4, 7, 12, 24, 35, 60, 110, 175, 258, 418, #784, 1158, 1920, 2964, 4784, 7466 #Average sequence: 2., 3., 4.500000000, 6., 7.428571429, 8.916666667, 10.75000000, 12.25714286, 13.50000000, 16.08181818, 18.11428571, 18.68217054, 21.19617225, 24.73724490, 26.29274611, 28.70885417, 31.10661269, 33.36099498, 36.87972140 PrefixBySizeTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i,n) AndFilters(AndFilters(stopcond(i), MakeAtLeastTPrefixFilter(1)), MakeSizeNFilter(n)): end: OpenDB("data.txt"): ResetDB("data.txt"): return seq([ParallelCountAverageFileNoReset("data.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i)], [seq(LSelector,n=1..i)],stopcond(i))],i=7..cap): end: ##DATA #(all sequences start at n+4, everything earlier is zeroes) #HEY! That's something I can try to prove! #3 Count sequence: 1, 2, 4, 3, 8, 9, 14, 11, 21, 19, 31, 29, 41 #4 Count sequence: 2, 1, 10, 13, 26, 34, 51, 73, 102, 138, 181, 220 #5 Count sequence: 5, 10, 30, 51, 95, 145, 218, 350, 505, 707, 967 #6 Count sequence: 6, 25, 66, 134, 299, 453, 808, 1265, 2000, 2904 #7 Count sequence: 14, 52, 131, 355, 614, 1354, 2338, 4041, 6397 #8 Count sequence: 19, 98, 298, 612, 1584, 3173, 6200, 10823 #9 Count sequence: 35, 157, 491, 1382, 3221, 7224, 14287 #10 Count sequence: 39, 243, 881, 2501, 6408, 14516 #11 Count sequence: 55, 348, 1476, 4372, 11551 #12 Count sequence: 64, 547, 2201, 7324 #13 Count sequence: 94, 705, 3456 #14 Count sequence: 104, 1027 #15 Count sequence: 142 # #3 Average sequence: 3., 5., 5., 12.33333333, 9.750000000, 14.77777778, 9.857142857, 15.45454545, 14.76190476, 18.47368421, 16.32258065, 18.34482759, 20.17073171 #4 Average sequence: 10., 8., 10.30000000, 12.23076923, 17.92307692, 14.67647059, 20.23529412, 18.50684932, 24.30392157, 26.81159420, 27.47513812, 26.17272727 #5 Average sequence: 16.20000000, 7.800000000, 13.10000000, 18.50980392, 18.51578947, 19.55172414, 23.73394495, 25.44857143, 26.56237624, 29.63366337, 30.88831437 #6 Average sequence: 17.50000000, 14.64000000, 19.68181818, 20.10447761, 20.62207358, 25.06401766, 27.02722772, 27.99209486, 30.50250000, 31.81852617 #7 Average sequence: 14.71428571, 22.30769231, 18.78625954, 21.18309859, 24.62214984, 26.65878877, 28.85158255, 32.10566691, 33.27200250 #8 Average sequence: 24.89473684, 23.11224490, 23.00335570, 23.66013072, 26.72159091, 28.86038449, 31.80161290, 34.47075672 #9 Average sequence: 23.14285714, 23.33757962, 23.76578411, 28.28654124, 28.32629618, 31.48435770, 35.40680339 #10 Average sequence: 23.79487179, 25.44032922, 29.68217934, 28.81567373, 31.45568040, 34.82088730 #11 Average sequence: 24.87272727, 32.33620690, 30.13753388, 32.74428179, 33.86529305 #12 Average sequence: 33.34375000, 30.63436929, 34.98682417, 34.40961223 #13 Average sequence: 31.44680851, 37.91063830, 35.03703704 #14 Average sequence: 37.43269231, 35.62999026 #15 Average sequence: 35.98591549 PrefixBySizePrimTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i,n) AndFilters(AndFilters(stopcond(i), MakeAtLeastTPrefixFilter(1)), MakeSizeNFilter(n)): end: OpenDB("dataprim.txt"): ResetDB("dataprim.txt"): return seq([ParallelCountAverageFileNoReset("dataprim.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i)], [seq(LSelector,n=1..i)],stopcond(i))],i=7..cap): end: ##DATA #(all sequences start at n+4, everything earlier is zeroes) #3 Count sequence: 1, 2, 4, 3, 8, 9, 14, 10, 21, 17, 31, 25, 41 #4 Count sequence: 2, 1, 9, 12, 24, 28, 50, 65, 91, 127, 165, 202 #5 Count sequence: 5, 9, 25, 43, 86, 128, 190, 299, 444, 607, 855 #6 Count sequence: 5, 18, 48, 95, 225, 358, 612, 970, 1541, 2239 #7 Count sequence: 10, 38, 91, 222, 427, 945, 1630, 2812, 4575 #8 Count sequence: 8, 57, 154, 342, 935, 1881, 3802, 7058 #9 Count sequence: 13, 69, 222, 697, 1565, 3809, 7894 #10 Count sequence: 8, 90, 375, 1050, 2807, 6850 #11 Count sequence: 15, 120, 538, 1729, 4612 #12 Count sequence: 14, 141, 791, 2547 #13 Count sequence: 17, 215, 1009 #14 Count sequence: 27, 239 #15 Count sequence: 25 # #3 Average sequence: 3., 5., 5., 12.33333333, 9.750000000, 14.77777778, 9.857142857, 16.40000000, 14.76190476, 19.47058824, 16.32258065, 19.68000000, 20.17073171 #4 Average sequence: 10., 8., 11.11111111, 12.83333333, 18.29166667, 16.39285714, 20.12000000, 19.29230769, 25.49450549, 27.72440945, 28.70303030, 26.79702970 #5 Average sequence: 16.20000000, 8., 14.48000000, 19.86046512, 19.03488372, 19.71875000, 24.92631579, 26.18394649, 27.95045045, 31.09060956, 31.75438596 #6 Average sequence: 20.20000000, 14.88888889, 22.08333333, 21.93684211, 22.37333333, 26.79608939, 29.32026144, 30.36701031, 32.50486697, 34.34613667 #7 Average sequence: 17.80000000, 23.21052632, 21.13186813, 24.54054054, 26.96487119, 28.85185185, 31.80981595, 35.64011380, 37.19475410 #8 Average sequence: 34., 27.45614035, 30.26623377, 26.33040936, 30.39679144, 32.81552366, 36.05970542, 39.19552281 #9 Average sequence: 27.23076923, 27.75362319, 27.31981982, 34.94404591, 33.50223642, 36.95300604, 42.09399544 #10 Average sequence: 21.37500000, 30.50000000, 36.34666667, 35.67333333, 38.72212326, 42.57591241 #11 Average sequence: 30.66666667, 36.90000000, 38.64684015, 41.35106998, 43.22658283 #12 Average sequence: 34.21428571, 42.00709220, 44.30847029, 46.33686690 #13 Average sequence: 43.23529412, 49.38604651, 48.40237859 #14 Average sequence: 44.62962963, 51.16317992 #15 Average sequence: 53.20000000 PrefixBySizeNonContTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i,n) AndFilters(AndFilters(AndFilters(stopcond(i), MakeAtLeastTPrefixFilter(1)), MakeSizeNFilter(n)), PrimitiveFilter): end: OpenDB("data.txt"): ResetDB("data.txt"): return seq([ParallelCountAverageFileNoReset("data.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i)], [seq(LSelector,n=1..i)],stopcond(i))],i=7..cap): end: ##DATA #(all sequences start at n+4, everything earlier is zeroes) #This data set is very similar to the previous one #3 Count sequence: 1, 2, 4, 3, 8, 9, 14, 11, 21, 19, 31, 29, 41 #4 Count sequence: 2, 1, 9, 12, 24, 28, 50, 65, 93, 127, 166, 202 #5 Count sequence: 5, 9, 25, 43, 86, 128, 190, 299, 444, 612, 855 #6 Count sequence: 5, 18, 48, 95, 225, 358, 612, 970, 1541, 2239 #7 Count sequence: 10, 38, 91, 222, 427, 945, 1630, 2812, 4575 #8 Count sequence: 8, 57, 154, 342, 935, 1881, 3802, 7058 #9 Count sequence: 13, 69, 222, 697, 1565, 3809, 7894 #10 Count sequence: 8, 90, 375, 1050, 2807, 6850 #11 Count sequence: 15, 120, 538, 1729, 4612 #12 Count sequence: 14, 141, 791, 2547 #13 Count sequence: 17, 215, 1009 #14 Count sequence: 27, 239 #15 Count sequence: 25 # #3 Average sequence: 3., 5., 5., 12.33333333, 9.750000000, 14.77777778, 9.857142857, 15.45454545, 14.76190476, 18.47368421, 16.32258065, 18.34482759, 20.17073171 #4 Average sequence: 10., 8., 11.11111111, 12.83333333, 18.29166667, 16.39285714, 20.12000000, 19.29230769, 25.37634409, 27.72440945, 28.62650602, 26.79702970 #5 Average sequence: 16.20000000, 8., 14.48000000, 19.86046512, 19.03488372, 19.71875000, 24.92631579, 26.18394649, 27.95045045, 31.10130719, 31.75438596 #6 Average sequence: 20.20000000, 14.88888889, 22.08333333, 21.93684211, 22.37333333, 26.79608939, 29.32026144, 30.36701031, 32.50486697, 34.34613667 #7 Average sequence: 17.80000000, 23.21052632, 21.13186813, 24.54054054, 26.96487119, 28.85185185, 31.80981595, 35.64011380, 37.19475410 #8 Average sequence: 34., 27.45614035, 30.26623377, 26.33040936, 30.39679144, 32.81552366, 36.05970542, 39.19552281 #9 Average sequence: 27.23076923, 27.75362319, 27.31981982, 34.94404591, 33.50223642, 36.95300604, 42.09399544 #10 Average sequence: 21.37500000, 30.50000000, 36.34666667, 35.67333333, 38.72212326, 42.57591241 #11 Average sequence: 30.66666667, 36.90000000, 38.64684015, 41.35106998, 43.22658283 #12 Average sequence: 34.21428571, 42.00709220, 44.30847029, 46.33686690 #13 Average sequence: 43.23529412, 49.38604651, 48.40237859 #14 Average sequence: 44.62962963, 51.16317992 #15 Average sequence: 53.20000000 PrefixBySizeRelPrimeTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: filter:=proc(i,n) AndFilters(AndFilters(AndFilters(stopcond(i), MakeAtLeastTPrefixFilter(1)), MakeSizeNFilter(n)), RelPrimeFilter): end: OpenDB("data.txt"): ResetDB("data.txt"): return seq([ParallelCountAverageFileNoReset("data.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i)], [seq(LSelector,n=1..i)],stopcond(i))],i=7..cap): end: ##DATA #(all sequences start at n+4, everything earlier is zeroes) #Very similar to the first data set #3 Count sequence: 1, 2, 4, 3, 8, 9, 14, 10, 21, 17, 31, 25, 41 #4 Count sequence: 2, 1, 10, 13, 26, 34, 51, 73, 100, 138, 180, 220 #5 Count sequence: 5, 10, 30, 51, 95, 145, 218, 350, 505, 702, 967 #6 Count sequence: 6, 25, 66, 134, 299, 453, 808, 1265, 2000, 2904 #7 Count sequence: 14, 52, 131, 355, 614, 1354, 2338, 4041, 6397 #8 Count sequence: 19, 98, 298, 612, 1584, 3173, 6200, 10823 #9 Count sequence: 35, 157, 491, 1382, 3221, 7224, 14287 #10 Count sequence: 39, 243, 881, 2501, 6408, 14516 #11 Count sequence: 55, 348, 1476, 4372, 11551 #12 Count sequence: 64, 547, 2201, 7324 #13 Count sequence: 94, 705, 3456 #14 Count sequence: 104, 1027 #15 Count sequence: 142 # #3 Average sequence: 3., 5., 5., 12.33333333, 9.750000000, 14.77777778, 9.857142857, 16.40000000, 14.76190476, 19.47058824, 16.32258065, 19.68000000, 20.17073171 #4 Average sequence: 10., 8., 10.30000000, 12.23076923, 17.92307692, 14.67647059, 20.23529412, 18.50684932, 24.39000000, 26.81159420, 27.53888889, 26.17272727 #5 Average sequence: 16.20000000, 7.800000000, 13.10000000, 18.50980392, 18.51578947, 19.55172414, 23.73394495, 25.44857143, 26.56237624, 29.61396011, 30.88831437 #6 Average sequence: 17.50000000, 14.64000000, 19.68181818, 20.10447761, 20.62207358, 25.06401766, 27.02722772, 27.99209486, 30.50250000, 31.81852617 #7 Average sequence: 14.71428571, 22.30769231, 18.78625954, 21.18309859, 24.62214984, 26.65878877, 28.85158255, 32.10566691, 33.27200250 #8 Average sequence: 24.89473684, 23.11224490, 23.00335570, 23.66013072, 26.72159091, 28.86038449, 31.80161290, 34.47075672 #9 Average sequence: 23.14285714, 23.33757962, 23.76578411, 28.28654124, 28.32629618, 31.48435770, 35.40680339 #10 Average sequence: 23.79487179, 25.44032922, 29.68217934, 28.81567373, 31.45568040, 34.82088730 #11 Average sequence: 24.87272727, 32.33620690, 30.13753388, 32.74428179, 33.86529305 #12 Average sequence: 33.34375000, 30.63436929, 34.98682417, 34.40961223 #13 Average sequence: 31.44680851, 37.91063830, 35.03703704 #14 Average sequence: 37.43269231, 35.62999026 #15 Average sequence: 35.98591549 BySizePrimTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: OpenDB("dataprim.txt"): ResetDB("dataprim.txt"): filter:=proc(i,n) AndFilters(stopcond(i), MakeSizeNFilter(n)): end: return seq([ParallelCountAverageFileNoReset("dataprim.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i), seq(filter(i,n),n=1..i)],[seq(LSelector,n=1..i), seq(GSelector,n=1..i)],stopcond(i))],i=1..cap): end: ##DATA #(all sequences start at n, everything earlier is zeroes) #1 Count sequence: 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 #2 Count sequence: 1, 1, 2, 3, 2, 5, 4, 5, 4, 9, 4, 11, 6, 7, 8, 15, 6, 17 #3 Count sequence: 1, 1, 3, 5, 8, 10, 15, 18, 26, 27, 38, 39, 53, 54, 73, 66, 95 #4 Count sequence: 1, 0, 3, 8, 11, 19, 31, 48, 63, 98, 119, 169, 191, 272, 304, 419 #5 Count sequence: 1, 1, 3, 11, 23, 36, 66, 111, 169, 256, 382, 509, 747, 967, 1283 #6 Count sequence: 1, 0, 1, 6, 35, 55, 94, 178, 380, 566, 927, 1405, 2115, 3072 #7 Count sequence: 1, 1, 1, 9, 36, 96, 165, 393, 675, 1323, 2146, 3630, 5664 #8 Count sequence: 1, 0, 1, 6, 26, 108, 285, 511, 1270, 2448, 4669, 8306 #9 Count sequence: 1, 1, 1, 4, 31, 141, 353, 981, 2020, 4585, 9181 #10 Count sequence: 1, 0, 1, 2, 24, 136, 546, 1331, 3434, 7851 #11 Count sequence: 1, 1, 1, 4, 32, 185, 690, 2115, 5339 #12 Count sequence: 1, 0, 1, 2, 24, 183, 916, 2921 #13 Count sequence: 1, 1, 1, 4, 24, 264, 1136 #14 Count sequence: 1, 0, 1, 2, 36, 292 #15 Count sequence: 1, 1, 1, 4, 32 #16 Count sequence: 1, 0, 1, 2 #17 Count sequence: 1, 1, 1 #18 Count sequence: 1, 0 #19 Count sequence: 1 # #2 Average period sequence: 3., 5., 6., 8., 9., 11., 12., 14.20000000, 15., 17., 18., 20., 21., 23.42857143, 24., 26., 27., 29. #3 Average period sequence: 4., 7., 7.333333333, 9.400000000, 11., 10.50000000, 11.26666667, 17., 16.42307692, 16.55555556, 17.60526316, 20.07692308, 21.37735849, 25.48148148, 23.64383562, 26.12121212, 27.93684211 #4 Average period sequence: 5., -1., 8.333333333, 9.875000000, 13.54545455, 13.84210526, 14.45161290, 17.62500000, 19.87301587, 20.25510204, 24.05882353, 22.79881657, 27.68586387, 29.68014706, 30.26973684, 30.68973747 #5 Average period sequence: 6., 10., 10.33333333, 11.27272727, 13.69565217, 14.41666667, 16.48484848, 18.94594595, 20.07692308, 21.73828125, 24.70680628, 26.69548134, 28.47657296, 30.60186143, 32.58846454 #6 Average period sequence: 7., -1., 11., 12.83333333, 16.48571429, 17.78181818, 20.05319149, 21.76404494, 23.39473684, 28.13427562, 29.40992449, 30.31886121, 32.44539007, 34.11067708 #7 Average period sequence: 8., 13., 14., 14.22222222, 16.55555556, 20.76041667, 21.71515152, 24.69974555, 27.00592593, 28.61678005, 31.80102516, 35.37355372, 36.95639124 #8 Average period sequence: 9., -1., 14., 15.50000000, 22.61538462, 23.45370370, 28.48070175, 26.52250489, 30.53543307, 32.61151961, 35.77682587, 38.87274260 #9 Average period sequence: 10., 16., 17., 17.75000000, 22.22580645, 25.64539007, 25.74220963, 33.02650357, 33.32425743, 36.37818975, 41.44515848 #10 Average period sequence: 11., -1., 17., 20., 21.20833333, 28.35294118, 33.73992674, 34.83320811, 37.86866628, 42.32798370 #11 Average period sequence: 12., 19., 20., 21., 25.18750000, 32.78378378, 36.16666667, 39.83120567, 42.53343323 #12 Average period sequence: 13., -1., 20., 23.50000000, 30.37500000, 39.53005464, 43.08406114, 45.32488874 #13 Average period sequence: 14., 22., 23., 24.25000000, 37.70833333, 45.37121212, 47.11091549 #14 Average period sequence: 15., -1., 23., 27., 40.77777778, 47.59246575 #15 Average period sequence: 16., 25., 26., 27.50000000, 47.56250000 #16 Average period sequence: 17., -1., 26., 30.50000000 #17 Average period sequence: 18., 28., 29. # #(these start at n+4) #3 Average prefix sequence: 1., 2.300000000, 4., 2.333333333, 6.153846154, 5.407407407, 9.447368421, 6.333333333, 11.75471698, 8.925925926, 17.31506849, 14.30303030, 19.78947368 #4 Average prefix sequence: 2., 0.5263157895, 5., 3.979166667, 8., 7.316326531, 11.95798319, 11.37278107, 16.79581152, 15.99264706, 22.56578947, 21.93556086 #5 Average prefix sequence: 3.869565217, 3.472222222, 6.954545455, 8.765765766, 13., 13.50000000, 16.33507853, 20.37917485, 22.73627845, 26.17580145, 31.08729540 #6 Average prefix sequence: 2.085714286, 7.181818182, 14.22340426, 15.51685393, 20.70263158, 22.98056537, 27.27400216, 31.67971530, 36.63971631, 39.87727865 #7 Average prefix sequence: 5.583333333, 10.68750000, 17.23030303, 19.73027990, 24.47851852, 31.03325775, 37.36067102, 43.72589532, 50.04996469 #8 Average prefix sequence: 9.692307692, 18.35185185, 19.92982456, 26.33855186, 35.66220472, 41.32271242, 51.60655387, 59.53660005 #9 Average prefix sequence: 18.03225806, 21.06382979, 26.58923513, 35.47502548, 46.24801980, 56.59651036, 66.75318593 #10 Average prefix sequence: 11.54166667, 36.61764706, 38.42490842, 48.13899324, 58.96359930, 71.42007388 #11 Average prefix sequence: 21.18750000, 42.47567568, 50.83623188, 61.99952719, 72.46225885 #12 Average prefix sequence: 37.75000000, 58.51912568, 69.12772926, 76.19753509 #13 Average prefix sequence: 46.33333333, 67.81818182, 83.25352113 #14 Average prefix sequence: 59.19444444, 78.67465753 #15 Average prefix sequence: 61.62500000 BySizeNoContTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: OpenDB("data.txt"): ResetDB("data.txt"): filter:=proc(i,n) AndFilters(AndFilters(stopcond(i), MakeSizeNFilter(n)),PrimitiveFilter): end: return seq([ParallelCountAverageFileNoReset("data.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i), seq(filter(i,n),n=1..i)],[seq(LSelector,n=1..i), seq(GSelector,n=1..i)],stopcond(i))],i=1..cap): end: #Trying to find an OEIS sequence with this one BySizeRelPrimeTest:=proc(cap) local filter,filters,stopcond,i,n: stopcond:=proc(i) MakeMaxNFilter(i): end: OpenDB("data.txt"): ResetDB("data.txt"): filter:=proc(i,n) AndFilters(AndFilters(stopcond(i), MakeSizeNFilter(n)),RelPrimeFilter): end: return seq([ParallelCountAverageFileNoReset("data.txt", [seq(filter(i,n),n=1..i)],[seq(filter(i,n),n=1..i), seq(filter(i,n),n=1..i)],[seq(LSelector,n=1..i), seq(GSelector,n=1..i)],stopcond(i))],i=1..cap): end: