cp's OEIS Frontend

A363770 Integers k such that the number of binary partitions of k is not a sum of three squares.

%I A363770 #30 Aug 02 2023 12:05:38
%S A363770 20,21,36,37,68,69,80,81,116,117,132,133,144,145,180,181,212,213,228,
%T A363770 229,260,261,272,273,308,309,320,321,340,341,356,357,404,405,420,421,
%U A363770 452,453,464,465,500,501,516,517,528,529,564,565,576,577,596,597,612,613,660,661,676,677
%N A363770 Integers k such that the number of binary partitions of k is not a sum of three squares.
%C A363770 An infinite sequence.
%H A363770 Bartosz Sobolewski and Maciej Ulas, <a href="https://arxiv.org/abs/2211.16622">Values of binary partition function represented by a sum of three squares</a>, arXiv:2211.16622 [math.NT], 2023.
%F A363770 Each term is equal to 2*b(m) or 2*b(m)+1 for some m, where b(m) = A363769(m).
%e A363770 a(1)=20 because b(20)=60 is not a sum of three squares and for i=1, ..., 19, the numbers b(i), i=1,...,19 are sums of three squares, where b(i) is the number of binary partitions of n.
%t A363770 bin[n_] :=
%t A363770  bin[n] =
%t A363770   If[n == 0, 1,
%t A363770    If[Mod[n, 2] == 0, bin[n - 1] + bin[n/2],
%t A363770     If[Mod[n, 2] == 1, bin[n - 1]]]];
%t A363770 B := {}; Do[
%t A363770  If[Mod[bin[n]/4^IntegerExponent[bin[n], 4], 8] == 7,
%t A363770   AppendTo[B, n]], {n, 1000}];
%t A363770 B
%Y A363770 Cf. A004215, A018819, A363769.
%K A363770 nonn,easy
%O A363770 1,1
%A A363770 _Maciej Ulas_, Jun 21 2023