A234366 Primes of the form q(p) + 1, where p is a prime and q(.) is the strict partition function (A000009).

2, 3, 13, 19, 257, 761, 2591, 32993, 70489, 173683, 570079, 3725411, 5010689, 132535703, 150473569, 406072423, 3328423937, 26114971541, 519999315041, 4743946406977, 704890732521793, 445433800804233383, 712827068077888961

Offset: 1

Author

Zhi-Wei Sun, Dec 28 2013

Keywords

• nonn

Comments

Though the primes in this sequence are very rare, by the conjecture in A234514 there should be infinitely many such primes.

Examples

			 a(1) = 2 since 2 = q(2) + 1 with 2 prime.
a(2) = 3 since 3 = q(3) + 1 with 3 prime.
a(3) = 13 since 13 = q(11) + 1 with 11 and 13 both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A000009, A000040, A234514, A234530

Programs

Mathematica

p[n_]:=A234530(n)
Table[PartitionsQ[p[n]]+1,{n,1,35}]

Formula

a(n) = A000009(A234530(n)) + 1.