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%I #11 Feb 08 2022 12:03:50
%S 181,32341,52021,96907,97171,100981,109507,192601,194671,238237,
%T 280627,304651,320911,418321,449971,547537,579961,626191,668611,
%U 767857,769807,771091,806107,885097,954157,991381,993247,1028047,1075357,1259677,1285021,1368727,1414837,1415191,1425007,1449841
%N Primes p such that q=2*p^2-1, r=2*p*q-1 and 2*p*r-1 are also prime.
%C Subsequence of A224990, and more elementary version of A224626.
%H Harvey P. Dale, <a href="/A224991/b224991.txt">Table of n, a(n) for n = 1..500</a>
%t qr[p_]:=Module[{q=2p^2-1,r},r=2p*q-1;{q,r,2p*r-1}]; Select[Prime[ Range[ 120000]],AllTrue[qr[#],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 10 2015 *)
%o (PARI) forprime(p=1,2e6,isprime(q=2*p^2-1)&&isprime(r=2*p*q-1)&&isprime(2*p*r-1)&&print1(p","))
%Y Cf. A224626, A224990.
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 22 2013