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

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, 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, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 7, 1, 4, 0, 0, 0, 3, 0, 1, 0, 0, 0

Offset: 0

Author

Michel Marcus, Jul 14 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. D. Hirschhorn and M. V. Subbarao, On the parity of p(n), Acta Arith., L (1988), 355-356. See p. 2.

Crossrefs

Cf. A000041, A040051, A355677.

Programs

Mathematica

a[n_] := Module[{k = 0}, While[!OddQ[PartitionsP[16*k + n]], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Jul 14 2022 *)

PARI

a(n) = my(k=0); while (!(numbpart(16*k+n) % 2), k++); k;