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

0,6

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).

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 *)

Crossrefs

Cf. A000009, A000040, A239675.

Sequence in context: A352177 A277367 A239936 * A303755 A321279 A294882

Adjacent sequences: A239698 A239699 A239700 * A239702 A239703 A239704

Keyword

nonn

Author

Sean A. Irvine, Mar 24 2014

Status

approved