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The set N such that each positive integer can be written in the form s^2 + n, s>=0, n in N, in an odd number of ways.
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%I #6 Dec 10 2018 09:31:48

%S 2,5,6,8,13,14,15,16,18,19,20,21,22,27,28,31,35,36,39,40,45,46,49,53,

%T 54,59,60,63,64,65,66,67,68,69,70,72,79,80,83,84,85,86,89,90,97,101,

%U 102,107,108,113,114,117,118,119,120,127,137,138,149,150,153

%N The set N such that each positive integer can be written in the form s^2 + n, s>=0, n in N, in an odd number of ways.

%D Computed by Sam Taylor.

%H J. N. Cooper, D. Eichhorn and K. O'Bryant, <a href="http://arXiv.org/abs/math.NT/0506496">Reciprocals of binary power series</a>

%F The terms are the exponents in the expansion of 1/((1-x)S) read mod 2 where S = Sum_{s >= 0} x^{s^2}.

%t m = maxExponent = 13;

%t S = Sum[x^(s^2), {s, 0, m}];

%t (Exponent[#, x]& /@ (List @@ (Normal[1/((1-x)S) + O[x]^(m^2)] /. c_ x^p_ :> Mod[c, 2] x^p))) // Rest (* _Jean-François Alcover_, Dec 10 2018 *)

%Y Cf. A108345.

%K nonn

%O 1,1

%A _Nadia Heninger_, Dec 13 2007