A276517 - OEIS

%I #29 Dec 14 2016 11:06:24

%S 2,3,6,7,8,11,12,15,18,19,22,23,24,25,26,27,28,29,30,31,32,33,41,43,

%T 44,45,46,47,48,53,54,60,61,67,70,72,74,76,79,82,84,87,90,92,93,96,

%U 105,106,107,108,111,112,114,117,122,128,133,135,139,141,148,159

%N Indices k such that A276516(k) = 0.

%C This is different from A001422, first difference: a(14) = 25, A001422(14) = 27.

%C Conjecture: for k > 7169 there are no more terms in this sequence (tested for k < 10000000).

%H Vaclav Kotesovec, <a href="/A276517/b276517.txt">Table of n, a(n) for n = 1..173</a>

%e 3 is in the sequence because A276516(3) = 0

%e 4 is not in the sequence because A276516(4) = -1

%e 4222 is in the sequence because A276516(4222) = 0

%e 7169 is in the sequence because A276516(7169) = 0

%t nn = 100; A276516 = Rest[CoefficientList[Series[Product[(1-x^(k^2)), {k, nn}], {x, 0, nn^2}], x]]; Select[Range[nn^2], A276516[[#]]==0&]

%t nmax = 10000; nn = Floor[Sqrt[nmax]]+1; poly = ConstantArray[0, nn^2 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^2 + 1]], {j, nn^2, k^2, -1}];, {k, 2, nn}]; A276516 = Take[poly, {2, nmax+1}]; Select[Range[nmax], A276516[[#]]==0&]

%Y Cf. A001422, A001661, A276516, A279486, A279487.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Dec 12 2016