%I #8 Dec 29 2013 01:29:54

%S 2,5,11,17977,790738119649411319,2058791472042884901563,

%T 27833079238879849385687,8121368081058512888507057,

%U 675004412390512738195023734124239,1398703012615213588677365804960180341,16193798232344933888778097136641377589301,204931453786129197483756438132982529754356479553,3019564607799532159016586951616642980389816614848623,22757918197082858017617136646280039394687006502870793231847,1078734573992480956821414895441907729656949308800686938161281

%N Primes of the form P(p-1), where p is a prime and P(.) is the partition function (A000041).

%C Though the primes in this sequence are very rare, by the conjecture in A234567 there should be infinitely many such primes.

%C See A234569 for a list of known primes p with P(p-1) also prime.

%H Zhi-Wei Sun, <a href="/A234572/b234572.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = A000041(A234569(n)-1).

%e a(1) = 2 since 2 = P(3-1) with 2 and 3 both prime.

%e a(2) = 5 since 5 = P(5-1) with 5 prime.

%e a(3) = 11 since 11 = P(7-1) with 7 and 11 both prime.

%t p[n_]:= A234569(n)

%t Table[PartitionsP[p[n]-1],{n,1,15}]

%Y Cf. A000040, A000041, A049575, A233346, A234470, A234475, A234514, A234530, A234567, A234569

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Dec 28 2013