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Primes p such that q = 2*p^3-1 and 2*p*q^2-1 are both prime.
4

%I #20 Sep 08 2022 08:46:04

%S 181,199,4363,4549,14563,15073,15739,27361,27901,33469,34231,37123,

%T 46279,48271,48673,54193,56101,64591,64609,65539,65731,70183,70891,

%U 75703,75979,77659,77863,80953,94309,112573,114889,115153,117361,118189,135799,144751

%N Primes p such that q = 2*p^3-1 and 2*p*q^2-1 are both prime.

%C When A224610(i) = 1 then prime(i) is in this sequence.

%C Subsequence of A177104. - _R. J. Mathar_, Apr 19 2013

%H Pierre CAMI, <a href="/A224614/b224614.txt">Table of n, a(n) for n = 1..10000</a>

%t Reap[For[p = 2, p < 200000, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1], Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Apr 19 2013 *)

%t bpQ[n_]:=Module[{c=2n^3-1},AllTrue[{c,2n*c^2-1},PrimeQ]]; Select[ Prime[ Range[ 15000]],bpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 05 2015 *)

%o (Magma) [p: p in PrimesUpTo(180000) | IsPrime(q) and IsPrime(2*p*q^2-1) where q is 2*p^3-1 ]; // _Bruno Berselli_, Apr 19 2013

%Y Cf. A224610, A224613.

%K nonn

%O 1,1

%A _Pierre CAMI_, Apr 12 2013