A239701 Least k > 0 such that q(n)+k is prime, where q(n) is the number of strict partitions of n.

1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 5, 3, 1, 5, 3, 3, 8, 3, 5, 7, 2, 1, 1, 1, 11, 7, 7, 1, 9, 2, 5, 1, 13, 1, 4, 17, 1, 3, 7, 5, 5, 1, 7, 7, 1, 2, 1, 27, 19, 1, 1, 2, 11, 11, 3, 21, 3, 3, 3, 11, 11, 9, 17, 13, 20, 1, 1, 5, 7, 3, 17, 12

Offset: 0

Author

Sean A. Irvine, Mar 24 2014

Keywords

• nonn

Comments

Conjecture of Zhi-Wei Sun: a(n) <= n for n > 0.

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..9999
• Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014-2016. See Conjecture 4.1(i).

Crossrefs

Cf. A000009, A000040, A239675.

Programs

Mathematica

a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsQ[n] + k], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 19 2019 *)