cp's OEIS Frontend

A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k.

%I A240545 #11 Dec 15 2018 08:34:37
%S A240545 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,
%T A240545 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,
%U A240545 8,3,2,1,2,1,9,4,8,3,2,1,8,3,2
%N A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k.
%C A240545 Conjecture of Zhi-Wei Sun: a(n) < n for n > 7.
%C A240545 Verified up to 6*10^8. - _Sean A. Irvine_, Apr 07 2014
%H A240545 Sean A. Irvine, <a href="/A240545/b240545.txt">Table of n, a(n) for n = 0..9999</a>
%H A240545 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 A240545 a(7)=8 because k=8 is the smallest k such that 7+A000041(k) is prime.
%t A240545 a[n_] := For[k = 1, True, k++, If[PrimeQ[n + PartitionsP[k]], Return[k]]];
%t A240545 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Dec 15 2018 *)
%Y A240545 Cf. A000040, A000041, A238457, A239675.
%K A240545 nonn
%O A240545 0,1
%A A240545 _Sean A. Irvine_, Apr 07 2014