A370156 Primes p such that (p-2)/3 is prime and 3*p+2 is composite.

11, 41, 53, 71, 113, 131, 179, 251, 311, 449, 491, 521, 593, 599, 683, 701, 719, 773, 809, 881, 941, 1049, 1061, 1103, 1151, 1229, 1301, 1319, 1373, 1439, 1499, 1511, 1571, 1709, 1733, 1931, 2273, 2309, 2393, 2579, 2591, 2663, 2843, 2861, 2903, 3041, 3119

Offset: 1

Author

Clark Kimberling, Feb 10 2024

Keywords

• nonn

Comments

None of these primes are lucky (A000959). - Davide Rotondo, Feb 12 2025

Examples

			(11-2)/3 is a prime and 3*11+2 isn't.
		

Links

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

Crossrefs

Cf. A000040, A000959, A115058 (supersequence), A023208, A370157.

Programs

Maple

filter:= proc(p) isprime(p) and isprime((p-2)/3) and not isprime(3*p+2) end proc:
select(filter, [seq(i,i=5..10000,6)]); # Robert Israel, Feb 28 2025

Mathematica

Select[Prime[Range[500]], ! PrimeQ[3 # + 2] && PrimeQ[(# - 2)/3] &]

PARI

isok(p) = if (isprime(p), !isprime(3*p+2) && (((p%3) == 2) && isprime((p-2)/3))); \\ Michel Marcus, Feb 17 2024