A239936 Least k > 0 such that p(k)+q(n) is prime, where p(n) is the number of partitions of n and 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, 4, 3, 1, 4, 3, 3, 10, 3, 4, 5, 2, 1, 1, 1, 6, 5, 5, 1, 6, 2, 4, 1, 12, 1, 15, 13, 1, 3, 5, 4, 4, 1, 5, 5, 1, 2, 1, 12, 49, 1, 1, 2, 6, 6, 3, 14, 3, 3, 3, 6, 6, 16, 13, 16, 11, 1, 1, 4, 5, 3, 12, 25

Offset

0,6

Comments

Conjecture of Zhi-Wei Sun: a(n) < n for n > 1.

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(ii).

Example

a(5)=2 since q(5)+p(2)=3+2=5 is prime but q(5)+p(1)=4 is composite.

Mathematica

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

Crossrefs

Cf. A000009, A000040, A000041, A239675, A239736.

Sequence in context: A265575 A352177 A277367 * A239701 A303755 A321279

Adjacent sequences: A239933 A239934 A239935 * A239937 A239938 A239939

Keyword

nonn

Author

Sean A. Irvine, Mar 29 2014

Status

approved