A224627 Prime numbers p such that 2*p^3-1, 2*p*q^2-1, 2*p*r^2-1, and 2*p*s^2-1 are prime numbers.

19460899, 86276401, 87980803, 167646631, 300722029, 343507111, 479516311, 906597943, 998757829, 1031308249, 1112697199, 1311383431, 1962194053

Offset: 1

Author

Pierre CAMI, Apr 12 2013

Keywords

• nonn

Comments

Subsequence of A224612, p = prime(n) when A224612(n)=1.

Crossrefs

Cf. A224612, A224613, A224614, A224626.

Programs

Mathematica

Reap[ For[p = 2, p < 2*10^9, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1] && PrimeQ[s = 2*p*r^2 - 1] && PrimeQ[2*p*s^2 - 1], Print[p]; Sow[p]] ]][[2, 1]] (* Jean-François Alcover, Apr 22 2013 *)

Extensions

More terms from Jean-François Alcover, Apr 22 2013