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

Author

Zhi-Wei Sun, Dec 27 2013

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)