A224614 Primes p such that q = 2*p^3-1 and 2*p*q^2-1 are both prime.

181, 199, 4363, 4549, 14563, 15073, 15739, 27361, 27901, 33469, 34231, 37123, 46279, 48271, 48673, 54193, 56101, 64591, 64609, 65539, 65731, 70183, 70891, 75703, 75979, 77659, 77863, 80953, 94309, 112573, 114889, 115153, 117361, 118189, 135799, 144751

Offset: 1

Author

Pierre CAMI, Apr 12 2013

Keywords

• nonn

Comments

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

Subsequence of A177104. - R. J. Mathar, Apr 19 2013

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A224610, A224613.

Programs

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

Mathematica

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 *)
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 *)