A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k.

2, 1, 1, 2, 1, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 2, 1, 8, 3, 2, 1, 9, 4, 8, 3, 2, 1, 2, 1, 8, 4, 11, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 10, 4, 8, 3, 2, 1, 9, 4, 10, 3, 2, 1, 2, 1, 8, 4, 15, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 4, 8, 3, 2, 1, 8, 3, 2

Offset

0,1

Comments

Conjecture of Zhi-Wei Sun: a(n) < n for n > 7.

Verified up to 6*10^8. - Sean A. Irvine, Apr 07 2014

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, 2014. See Conjecture 4.1(ii).

Example

a(7)=8 because k=8 is the smallest k such that 7+A000041(k) is prime.

Mathematica

a[n_] := For[k = 1, True, k++, If[PrimeQ[n + PartitionsP[k]], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 15 2018 *)

Crossrefs

Cf. A000040, A000041, A238457, A239675.

Sequence in context: A080121 A122901 A001917 * A091591 A337633 A358492

Adjacent sequences: A240542 A240543 A240544 * A240546 A240547 A240548

Keyword

nonn

Author

Sean A. Irvine, Apr 07 2014

Status

approved