A234530 Primes p with q(p) + 1 also prime, where q(.) is the strict partition function (A000009).

2, 3, 11, 13, 29, 37, 47, 71, 79, 89, 103, 127, 131, 179, 181, 197, 233, 271, 331, 379, 499, 677, 691, 757, 887, 911, 1019, 1063, 1123, 1279, 1429, 1531, 1559, 1637, 2251, 2719, 3571, 4007, 4201, 4211, 4297, 4447, 4651, 4967, 5953, 6131, 7937, 8233, 8599, 8819, 9013, 11003, 11093, 11813, 12251, 12889, 12953, 13487, 13687, 15259

Offset

1,1

Comments

By the conjecture in A234514, this sequence should have infinitely many terms.

It seems that a(n+1) < a(n) + a(n-1) for all n > 4.

See A234366 for primes of the form q(p) + 1 with p prime.

See also A234644 for a similar sequence.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..150

Example

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

Mathematica

n=0; Do[If[PrimeQ[PartitionsQ[Prime[k]]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10^5}]
Select[Prime[Range[2000]], PrimeQ[PartitionsQ[#]+1]&] (* Harvey P. Dale, Apr 23 2017 *)

Crossrefs

Cf. A000009, A000040, A233346, A233393, A234366, A234470, A234475, A234514, A234567, A234569, A234572, A234615, A234644, A234647

Sequence in context: A215378 A078763 A157884 * A235632 A085306 A161322

Adjacent sequences: A234527 A234528 A234529 * A234531 A234532 A234533

Keyword

nonn

Author

Zhi-Wei Sun, Dec 27 2013

Status

approved