A224626 Primes p such that q=2*p^3-1, r=2*p*q^2-1, and s=2*p*r^2-1 are all prime.

27361, 65731, 167623, 424093, 1559449, 2389693, 3880633, 4683661, 5755921, 5780881, 6124411, 6840643, 7802959, 7822879, 7917769, 8876719, 9488683, 9640321, 9966139, 10392073, 10865083, 10988743, 12363991, 12457681, 12756253, 13471561, 14437561, 14508709, 14550331, 14839711, 15366223, 16574143

Offset

1,1

Comments

A prime p here is prime p(n) when A224611(n) = 1.

A subsequence of A224614. - M. F. Hasler, Apr 22 2013

Links

Pierre CAMI, Table of n, a(n) for n = 1..747

Mathematica

Reap[ For[p = 2, p < 2*10^7, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1] && PrimeQ[2*p*r^2 - 1], Print[p]; Sow[p]] ]][[2, 1]] (* Jean-François Alcover, Apr 22 2013 *)
apQ[n_]:=Module[{q=2n^3-1, r}, r=2n q^2-1; And@@PrimeQ[{q, r, 2n r^2-1}]]; Select[ Prime[Range[1100000]], apQ] (* Harvey P. Dale, Nov 24 2013 *)

Prog

(PFGW SCRIPT)
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
WRITE myf, t
GOTO a

Crossrefs

Cf. A224611, A224613, A224614.

Sequence in context: A234686 A064967 A168215 * A237296 A166224 A187533

Adjacent sequences: A224623 A224624 A224625 * A224627 A224628 A224629

Keyword

nonn

Author

Pierre CAMI, Apr 12 2013

Status

approved