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A243595 Primes p such that 3 + 2*p^2 is also prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 05:44 EDT 2021. Contains 343072 sequences. (Running on oeis4.)