%I
%S 5,11,13,17,19,23,41,43,53,59,79,103,151,191,269,277,283,373,419,521,
%T 571,577,607,829,859,1039,2503,2657,2819,3533,3671,4079,4153,4243,
%U 4517,4951,4987,5689,5737,5783,7723,8101,9137,9173,9241,9539,11467,12323,12697,15017,15277,15427,15803,16057,17959,18661
%N Primes p with q(p)  1 also prime, where q(.) is the strict partition function (A000009).
%C By the conjecture in A234615, this sequence should have infinitely many terms.
%C See A234647 for primes of the form q(p)  1 with p prime.
%C See also A234530 for a similar sequence.
%H ZhiWei Sun, <a href="/A234644/b234644.txt">Table of n, a(n) for n = 1..140</a>
%H Z.W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e a(1) = 5 since neither q(2)  1 = 0 nor q(3)  1 = 1 is prime, but q(5)  1 = 2 is prime.
%e a(2) = 11 since q(7)  1 = 4 is composite, but q(11)  1 = 11 is prime.
%t q[k_]:=q[k]=PrimeQ[PartitionsQ[Prime[k]]1]
%t n=0;Do[If[q[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10^5}]
%Y Cf. A000009, A000040, A234470, A234475, A234514, A234530, A234567, A234569, A234572, A234615, A234647.
%K nonn
%O 1,1
%A _ZhiWei Sun_, Dec 29 2013
