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A122429 Primes p such that q = 4p^2 + 1, r = 4q^2 + 1 and s = 4r^2 + 1 are all primes.

%I A122429 #20 Oct 19 2017 03:15:03
%S A122429 13,9833,41647,151607,264757,356123,361223,446863,449093,457813,
%T A122429 531383,641057,655927,841697,855947,899263,913687,1052813,1081757,
%U A122429 1379383,1506493,1575757,1685087,1821013,1821377,1981517,2054233,2142037
%N A122429 Primes p such that q = 4p^2 + 1, r = 4q^2 + 1 and s = 4r^2 + 1 are all primes.
%C A122429 Next terms up to 400000th prime are 2286877, 2524157, 2595247, 2621737, 2931583, 3023437, 3425843, 3428567, 3538517, 3705187, 3777883, 3799717, 3875143, 3913727, 3973553, 4019833, 4167073, 4249523, 4488167, 4651873, 4822193, 4914937, 5054167, 5108293, 5140147, 5465303, 5520007, 5542003. - _Zak Seidov_, Jan 16 2009
%C A122429 Subsequence of A122424. - _Pierre CAMI_, Jul 21 2014
%D A122429 Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., 2005, p.74.
%H A122429 Pierre CAMI, <a href="/A122429/b122429.txt">Table of n, a(n) for n = 1..3636</a>
%e A122429 13 is there because 13, 677, 1833317 and 13444204889957 are prime.
%t A122429 Reap[Do[p=Prime[n];q=4p^2+1;r=4q^2+1;s=4r^2+1;If[PrimeQ[{q,r,s}]=={True, True,True},Sow[p]],{n,15000}]][[2,1]]
%t A122429 Select[Prime[Range[200000]],AllTrue[NestList[4#^2+1&,#,3],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 22 2015 *)
%o A122429 (PARI)
%o A122429 f(x)=4*x^2+1;
%o A122429 forprime(p=1, 10^8, if(isprime(f(p))&&isprime(f(f(p)))&&isprime(f(f(f(p)))), print1(p, ", "))) \\ _Derek Orr_, Jul 31 2014
%Y A122429 Cf. A052291, A005574, A001912, A122424.
%K A122429 nonn
%O A122429 1,1
%A A122429 _Zak Seidov_, Oct 20 2006
%E A122429 More terms from _Don Reble_, Oct 24 2006
%E A122429 Edited by _R. J. Mathar_, Nov 02 2009