#The Calkin-Wilf construction for counting the rationals

Help:=proc() print(` CW(x) , CWlist(L) , CWseq1(n) `): end:

#CW(x): The two children (given a  pair) of the fraction x
CW:=proc(x) local a,b:

a:=numer(x):

b:=denom(x):

[a/(a+b),(a+b)/b]:

end:


#CWlist(L): the list, in order of all the Calkin-Wilf children
#of the list of fractions L
CWlist:=proc(L) local i:

[seq( op(CW(L[i])), i=1..nops(L) ) ]:

end:

#CWseq1(n): ALL the fractions in order, in the Calkin-Wilf
#tree arranged from generation to generation, and each generation
#is read from oldest to youngest for n generation
CWseq1:=proc(n) local i, G,L:

G:=[1]:


L:=[]:

for i from  0 to n-1 do

L:=[ op(L), op(G)]:

G:=CWlist(G):



od:

[seq(numer(L[i]),i=1..nops(L))]:


end: