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