A243595 Primes p such that 3 + 2*p^2 is also prime.

2, 5, 7, 23, 37, 43, 47, 83, 103, 107, 113, 127, 197, 373, 433, 463, 467, 523, 547, 587, 593, 617, 733, 743, 797, 863, 877, 887, 953, 1097, 1163, 1213, 1297, 1427, 1493, 1567, 1583, 1657, 1667, 1693, 1783, 1877, 1987, 2053, 2063, 2087, 2207, 2357, 2557, 2753

Offset

1,1

Comments

Corresponding primes 3 + 2*p^2 are congruent to 5 modulo 6.

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Example

2 is in the sequence because 3+2*2^2 = 11 is prime; also, for the comment, 11 = 6+5.
5 is in the sequence because 3+2*5^2 = 53 is prime, also 53 = 6*8+5.
7 is in the sequence because 3+2*7^2 = 101 is prime, also 101 = 6*16+5.

Mathematica

Select[Prime[Range[500]], PrimeQ[3 + 2 #^2] &] (* Bruno Berselli, Jun 07 2014 *)

Prog

(PARI) s=[]; forprime(p=2, 4000, if(isprime(3+2*p^2), s=concat(s, p))); s \\ Colin Barker, Jun 07 2014
(Magma) [p: p in PrimesUpTo(4000) | IsPrime(3+2*p^2)]; // Bruno Berselli, Jun 07 2014
(Sage) [p for p in primes(4000) if is_prime(3+2*p^2)] # Bruno Berselli, Jun 07 2014

Crossrefs

Cf. A002476, A033203, A153507, A161724.

Sequence in context: A279756 A103060 A256247 * A103807 A099228 A182474

Adjacent sequences: A243592 A243593 A243594 * A243596 A243597 A243598

Keyword

nonn,easy

Author

Zak Seidov, Jun 07 2014

Status

approved