login
a(n) such that the series 1/((1-x^a(1))(1-x^a(2))...)=1+x+x^8+x^27+...+x^(j^3)+... when read mod 2.
1

%I #11 Sep 14 2014 00:25:14

%S 1,2,4,9,10,11,12,13,14,15,18,19,22,23,25,26,27,30,37,38,40,41,42,44,

%T 45,48,51,52,53,54,55,56,58,59,64,67,68,70,71,72,73,74,79,82,83,84,86,

%U 88,89,93

%N a(n) such that the series 1/((1-x^a(1))(1-x^a(2))...)=1+x+x^8+x^27+...+x^(j^3)+... when read mod 2.

%t iend=150;

%t aim=CoefficientList[Sum[x^(i^3),{i,0,iend^(1/3)+1}],x];

%t c[1]=1;

%t index=1;

%t For[i=1,i<iend,i++,

%t ser=Mod[CoefficientList[Series[1/( Product[(1-x^c[j]),{j,1,index}] ),{x,0,iend+1}],x],2];

%t If[ser[[i+2]]!=aim[[i+2]],c[index+1]=i+1;index++]

%t ];

%t Table[c[i],{i,1,50}]

%K nonn

%O 1,2

%A _David S. Newman_, Aug 28 2014