cp's OEIS Frontend

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

%I A239736 #11 Dec 12 2018 03:16:51
%S A239736 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,
%T A239736 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,
%U A239736 8,27,9,23,3,7,2,24,36,38,9,26,16,1
%N A239736 Least k > 0 such that p(n)+p(k)-1 is prime, where p(n) is the number of partitions of n.
%C A239736 Conjecture of Zhi-Wei Sun: a(n) < n for n > 1.
%H A239736 Sean A. Irvine, <a href="/A239736/b239736.txt">Table of n, a(n) for n = 2..9999</a>
%H A239736 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014. See Conjecture 4.1(ii).
%e A239736 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.
%t A239736 a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[n] + PartitionsP[k] - 1], Return[k]]];
%t A239736 Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Dec 12 2018 *)
%o A239736 (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
%Y A239736 Cf. A000040, A000041, A239675.
%K A239736 nonn
%O A239736 2,6
%A A239736 _Sean A. Irvine_, Mar 25 2014