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A234569 Primes p with P(p-1) also prime, where P(.) is the partition function (A000041).

%I A234569 #61 Mar 14 2015 13:56:21
%S A234569 3,5,7,37,367,499,547,659,1087,1297,1579,2137,2503,3169,3343,4457,
%T A234569 4663,5003,7459,9293,16249,23203,34667,39971,41381,56383,61751,62987,
%U A234569 72661,77213,79697,98893,101771,127081,136193,188843,193811,259627,267187,282913,315467,320563,345923,354833,459029,482837,496477,548039,641419,647189
%N A234569 Primes p with P(p-1) also prime, where P(.) is the partition function (A000041).
%C A234569 By the conjecture in A234567, this sequence should have infinitely many terms. It seems that a(n+1) < a(n) + a(n-1) for all n > 5.
%C A234569 The b-file lists all terms not exceeding the 500000th prime 7368787. Note that P(a(113)-1) is a prime having 2999 decimal digits.
%C A234569 See also A234572 for primes of the form P(p-1) with p prime.
%H A234569 Zhi-Wei Sun, <a href="/A234569/b234569.txt">Table of n, a(n) for n = 1..113</a>
%H A234569 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A234569 a(1) = 3 since P(2-1) = 1 is not prime, but P(3-1) = 2 is prime.
%e A234569 a(2) = 5 since P(5-1) = 5 is prime.
%e A234569 a(3) = 7 since P(7-1) = 11 is prime.
%t A234569 n=0;Do[If[PrimeQ[PartitionsP[Prime[k]-1]],n=n+1;Print[n," ",Prime[k]]],{k,1,10^6}]
%Y A234569 Cf. A000040, A000041, A049575, A233346, A234470, A234475, A234514, A234530, A234567, A234572, A234615, A234644
%K A234569 nonn
%O A234569 1,1
%A A234569 _Zhi-Wei Sun_, Dec 28 2013