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A355676 a(n) is the least k such that p(16*k+n) is odd where p is the number of partitions A000041.

%I A355676 #16 Jul 15 2022 02:30:26
%S A355676 0,0,1,0,0,0,0,0,1,2,5,2,0,0,0,3,0,0,0,1,0,1,1,0,0,1,4,1,1,0,10,2,0,0,
%T A355676 3,0,0,0,0,0,1,0,3,0,0,1,9,1,0,0,2,0,0,0,0,1,0,1,2,2,0,0,8,0,5,1,1,0,
%U A355676 0,0,2,0,0,0,1,1,0,0,7,1,4,0,0,0,3,0,1,0,0,0
%N A355676 a(n) is the least k such that p(16*k+n) is odd where p is the number of partitions A000041.
%H A355676 Seiichi Manyama, <a href="/A355676/b355676.txt">Table of n, a(n) for n = 0..10000</a>
%H A355676 M. D. Hirschhorn and M. V. Subbarao, <a href="https://web.maths.unsw.edu.au/~mikeh/webpapers/paper27.pdf">On the parity of p(n)</a>, Acta Arith., L (1988), 355-356. See p. 2.
%t A355676 a[n_] := Module[{k = 0}, While[!OddQ[PartitionsP[16*k + n]], k++]; k]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 14 2022 *)
%o A355676 (PARI) a(n) = my(k=0); while (!(numbpart(16*k+n) % 2), k++); k;
%Y A355676 Cf. A000041, A040051, A355677.
%K A355676 nonn
%O A355676 0,10
%A A355676 _Michel Marcus_, Jul 14 2022