A338410 Primes p such that (p+2)/3 and (p+3)/2 are prime.

7, 19, 31, 139, 199, 211, 379, 499, 631, 919, 1039, 1291, 1399, 1759, 2179, 2719, 2731, 2971, 3271, 3691, 4591, 5791, 5851, 6079, 7591, 8011, 8779, 10039, 11299, 11719, 11731, 12979, 14251, 15031, 15511, 15679, 18451, 18859, 20071, 21379, 21559, 22051, 22639, 23599, 24499, 24691, 25339, 25579

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 25 2020

Keywords

• nonn

Comments

All terms == 7 (mod 12).

Examples

			a(3) = 31 is in the sequence because 31, (31+2)/3 = 11 and ((31+3)/2) = 17 are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A091180 and A092109.

Programs

Maple

filter:= t -> isprime(t) and isprime((t+2)/3) and isprime((t+3)/2):
select(filter, [seq(i,i=7..30000,12)]);

Mathematica

Select[Prime[Range[3000]],AllTrue[{(#+2)/3,(#+3)/2},PrimeQ]&] (* Harvey P. Dale, May 20 2023 *)

PARI

isok(p) = iferr(isprime(p) && isprime((p+2)/3) && isprime((p+3)/2), E, 0); \\ Michel Marcus, Oct 25 2020