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

Author

Zak Seidov, Oct 20 2006

Keywords

• nonn
• easy

Comments

Subsequence of A052291.

Links

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

Crossrefs

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

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

Programs

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

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 *)

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