

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
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OFFSET

2,6


COMMENTS

Conjecture of ZhiWei Sun: a(n) < n for n > 1.


LINKS

Sean A. Irvine, Table of n, a(n) for n = 2..9999
ZhiWei 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}] (* JeanFrançois 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



