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

1,1

Comments

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

Links

Table of n, a(n) for n=1..13.

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 *)

Prog

(PFGW & SCRIPTIFY)
SCRIPT
DIM n, 1
DIM q
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL a
SET n, n+1
SETS t, %d\,; p(n)
SET q, 2*p(n)^3-1
PRP q, t
IF ISPRP THEN GOTO b
GOTO a
LABEL b
SET q, 2*p(n)*q^2-1
PRP q, t
IF ISPRP THEN GOTO c
GOTO a
LABEL c
SET q, 2*p(n)*q^2-1
PRP q, t
IF ISPRP THEN GOTO d
GOTO a
LABEL d
SET q, 2*p(n)*q^2-1
PRP q, t
IF ISPRP THEN GOTO e
GOTO a
LABEL e
WRITE t, myf
GOTO a

Crossrefs

Cf. A224612, A224613, A224614, A224626.

Sequence in context: A184790 A183697 A022248 * A038683 A017287 A017395

Adjacent sequences: A224624 A224625 A224626 * A224628 A224629 A224630

Keyword

nonn

Author

Pierre CAMI, Apr 12 2013

Extensions

More terms from Jean-François Alcover, Apr 22 2013

Status

approved