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A239736 Least k > 0 such that p(n)+p(k)-1 is prime, where p(n) is the number of partitions of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A134653 A090207 A202538 * A065437 A097721 A073756

Adjacent sequences:  A239733 A239734 A239735 * A239737 A239738 A239739

KEYWORD

nonn

AUTHOR

Sean A. Irvine, Mar 25 2014

STATUS

approved

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Last modified December 14 07:03 EST 2019. Contains 329978 sequences. (Running on oeis4.)