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A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k. 2

%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-Fran├žois 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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Last modified April 12 10:52 EDT 2021. Contains 342920 sequences. (Running on oeis4.)