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
Keywords
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.
Programs
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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;