A122424 Primes p such that q = 4p^2 + 1 and r = 4q^2 + 1 are also prime.

3, 13, 47, 677, 983, 1013, 1163, 1373, 1567, 1877, 2003, 2333, 2477, 2753, 3463, 4057, 4423, 4993, 7253, 9833, 10993, 11383, 13907, 15413, 15607, 17317, 18517, 19867, 20123, 20533, 20693, 21937, 24517, 24967, 25633, 26293, 28547, 28867, 29063

Offset

1,1

Comments

Subsequence of A052291.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Maple

A122424:=n->`if`(isprime(n) and isprime(4*n^2+1) and isprime(4*(4*n^2+1)^2+1), n, NULL): seq(A122424(n), n=1..10^5); # Wesley Ivan Hurt, Aug 04 2014

Mathematica

Select[Prime[Range[3500]], PrimeQ[4 #^2 + 1] && PrimeQ[64 #^4 + 32 #^2 + 5]&] (* Vincenzo Librandi, Apr 09 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(30000) | IsPrime(q) and IsPrime(4*q^2+1) where q is 4*p^2+1]; // Vincenzo Librandi, Apr 09 2013
(PARI)
f(x)=4*x^2+1;
forprime(p=1, 10^5, if(isprime(f(p))&&isprime(f(f(p))), print1(p, ", "))) \\ Derek Orr, Jul 31 2014

Crossrefs

Cf. A052291 (Primes p such that 4p^2 + 1 is also prime).

Cf. A005574 (Numbers n such that n^2 + 1 is prime).

Sequence in context: A262322 A180278 A193164 * A027326 A108946 A352028

Adjacent sequences: A122421 A122422 A122423 * A122425 A122426 A122427

Keyword

nonn,easy

Author

Zak Seidov, Oct 20 2006

Status

approved