A362225 Primes of the form (2*p^2 + 1)/3 where p is a prime > 3.

17, 113, 193, 241, 353, 641, 1873, 3361, 5281, 8513, 10753, 16433, 17713, 18593, 21841, 25873, 34961, 80273, 92753, 107201, 111521, 117041, 134401, 158113, 168673, 172721, 182353, 195121, 211313, 217361, 221953, 239201, 279073, 376001, 394241

Offset: 1

Author

Alain Rocchelli, Apr 11 2023

Keywords

• nonn

Comments

The corresponding p values are the odd terms of A175256.

Examples

			17 is a term since for p=5, (2*p^2 + 1)/3 = (2*5^2 + 1)/3 = 17 and 17 is prime.
		

Crossrefs

Cf. A175255, A175256.

Programs

Mathematica

Select[(2*Prime[Range[3, 140]]^2 + 1)/3, PrimeQ] (* Amiram Eldar, May 18 2023 *)

PARI

forprime(p=5, 1000, my(Ap=floor((2*p^2+1)/3)); if(isprime(Ap), print1(Ap,", ")))

Formula

a(n) = (2*A175255(n+1)+1)/3.