A224991 Primes p such that q=2*p^2-1, r=2*p*q-1 and 2*p*r-1 are also prime.

181, 32341, 52021, 96907, 97171, 100981, 109507, 192601, 194671, 238237, 280627, 304651, 320911, 418321, 449971, 547537, 579961, 626191, 668611, 767857, 769807, 771091, 806107, 885097, 954157, 991381, 993247, 1028047, 1075357, 1259677, 1285021, 1368727, 1414837, 1415191, 1425007, 1449841

Offset: 1

Author

M. F. Hasler, Apr 22 2013

Keywords

• nonn

Comments

Subsequence of A224990, and more elementary version of A224626.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A224626, A224990.

Programs

Mathematica

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 *)

PARI

forprime(p=1,2e6,isprime(q=2*p^2-1)&&isprime(r=2*p*q-1)&&isprime(2*p*r-1)&&print1(p","))