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A239701 Least k > 0 such that q(n)+k is prime, where q(n) is the number of strict partitions of n.

%I A239701 #14 Feb 19 2019 09:21:12
%S A239701 1,1,1,1,1,2,1,2,1,3,1,1,2,1,1,2,5,3,1,5,3,3,8,3,5,7,2,1,1,1,11,7,7,1,
%T A239701 9,2,5,1,13,1,4,17,1,3,7,5,5,1,7,7,1,2,1,27,19,1,1,2,11,11,3,21,3,3,3,
%U A239701 11,11,9,17,13,20,1,1,5,7,3,17,12
%N A239701 Least k > 0 such that q(n)+k is prime, where q(n) is the number of strict partitions of n.
%C A239701 Conjecture of Zhi-Wei Sun: a(n) <= n for n > 0.
%H A239701 Sean A. Irvine, <a href="/A239701/b239701.txt">Table of n, a(n) for n = 0..9999</a>
%H A239701 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014-2016. See Conjecture 4.1(i).
%t A239701 a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsQ[n] + k], Return[k]]];
%t A239701 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 19 2019 *)
%Y A239701 Cf. A000009, A000040, A239675.
%K A239701 nonn
%O A239701 0,6
%A A239701 _Sean A. Irvine_, Mar 24 2014