cp's OEIS Frontend

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

%I A122424 #23 Sep 08 2022 08:45:28
%S A122424 3,13,47,677,983,1013,1163,1373,1567,1877,2003,2333,2477,2753,3463,
%T A122424 4057,4423,4993,7253,9833,10993,11383,13907,15413,15607,17317,18517,
%U A122424 19867,20123,20533,20693,21937,24517,24967,25633,26293,28547,28867,29063
%N A122424 Primes p such that q = 4p^2 + 1 and r = 4q^2 + 1 are also prime.
%C A122424 Subsequence of A052291.
%H A122424 Pierre CAMI, <a href="/A122424/b122424.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)
%p A122424 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
%t A122424 Select[Prime[Range[3500]], PrimeQ[4 #^2 + 1] && PrimeQ[64 #^4 + 32 #^2 + 5]&] (* _Vincenzo Librandi_, Apr 09 2013 *)
%o A122424 (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
%o A122424 (PARI)
%o A122424 f(x)=4*x^2+1;
%o A122424 forprime(p=1,10^5,if(isprime(f(p))&&isprime(f(f(p))),print1(p,", "))) \\ _Derek Orr_, Jul 31 2014
%Y A122424 Cf. A052291 (Primes p such that 4p^2 + 1 is also prime).
%Y A122424 Cf. A005574 (Numbers n such that n^2 + 1 is prime).
%K A122424 nonn,easy
%O A122424 1,1
%A A122424 _Zak Seidov_, Oct 20 2006