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

1,1

Comments

It seems that this sequence contains infinitely many terms.

See also A234569 for a similar sequence.

Links

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A067799 A321362 A230372 * A117702 A041343 A229349

Adjacent sequences: A234897 A234898 A234899 * A234901 A234902 A234903

Keyword

nonn

Author

Zhi-Wei Sun, Jan 01 2014

Status

approved