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A122424
Primes p such that q = 4p^2 + 1 and r = 4q^2 + 1 are also prime.
3
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
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Oct 20 2006
STATUS
approved