A239736 Least k > 0 such that p(n)+p(k)-1 is prime, where p(n) is the number of partitions of n.

1, 1, 1, 1, 1, 3, 2, 2, 2, 10, 3, 1, 3, 8, 3, 6, 4, 2, 4, 9, 9, 4, 4, 8, 2, 2, 2, 3, 11, 8, 4, 13, 19, 4, 1, 6, 3, 4, 2, 4, 26, 12, 5, 11, 11, 9, 6, 5, 25, 4, 24, 6, 4, 2, 5, 9, 9, 2, 7, 4, 28, 13, 8, 27, 9, 23, 3, 7, 2, 24, 36, 38, 9, 26, 16, 1

Offset

2,6

Comments

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

Links

Sean A. Irvine, Table of n, a(n) for n = 2..9999

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014. See Conjecture 4.1(ii).

Example

a(7)=3, since p(7)+p(1)-1=15 and p(7)+p(2)-1=16 are composite, but p(7)+p(3)-1=17 is prime.

Mathematica

a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[n] + PartitionsP[k] - 1], Return[k]]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 12 2018 *)

Prog

(PARI) s=[]; for(n=2, 100, k=1; while(!isprime(numbpart(n)+numbpart(k)-1), k++); s=concat(s, k)); s \\ Colin Barker, Mar 26 2014

Crossrefs

Cf. A000040, A000041, A239675.

Sequence in context: A090207 A364571 A202538 * A065437 A097721 A073756

Adjacent sequences: A239733 A239734 A239735 * A239737 A239738 A239739

Keyword

nonn

Author

Sean A. Irvine, Mar 25 2014

Status

approved