A234900 Primes p with P(p+1) also prime, where P(.) is the partition function (A000041).

2, 3, 5, 131, 167, 211, 439, 2731, 3167, 3541, 4261, 7457, 8447, 18289, 22669, 23201, 23557, 35401, 44507, 76781, 88721, 108131, 126097, 127079, 136319, 141359, 144139, 159169, 164089, 177487, 202627, 261757, 271181, 282911, 291971, 307067, 320561, 389219, 481589, 482627, 602867, 624259, 662107, 682361, 818887, 907657, 914189, 964267, 1040191, 1061689

Offset: 1

Author

Zhi-Wei Sun, Jan 01 2014

Keywords

• nonn

Comments

It seems that this sequence contains infinitely many terms.

See also A234569 for a similar sequence.

Examples

			a(1) = 2 since P(2+1) = 3 is prime.
a(2) = 3 since P(3+1) = 5 is prime.
a(3) = 5 since P(5+1) = 11 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A000040, A000041, A049575, A233346, A234470, A234514, A234530, A234567, A234569, A234615, A234644.

Programs

Mathematica

p[k_]:=p[k]=PrimeQ[PartitionsP[Prime[k]+1]]
n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10000}]