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A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A227796

Adjacent sequences:  A240542 A240543 A240544 * A240546 A240547 A240548

KEYWORD

nonn

AUTHOR

Sean A. Irvine, Apr 07 2014

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)