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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A224610, A224613.

Sequence in context: A159263 A159548 A206281 * A216309 A139648 A142519

Adjacent sequences: A224611 A224612 A224613 * A224615 A224616 A224617

Keyword

nonn

Author

Pierre CAMI, Apr 12 2013

Status

approved