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

1,1

Comments

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

Links

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

Formula

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

Example

 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.

Mathematica

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

Crossrefs

Cf. A000009, A000040, A234514, A234530

Sequence in context: A302485 A135118 A274905 * A084958 A249573 A295111

Adjacent sequences: A234363 A234364 A234365 * A234367 A234368 A234369

Keyword

nonn

Author

Zhi-Wei Sun, Dec 28 2013

Status

approved