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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified July 3 11:18 EDT 2022. Contains 355050 sequences. (Running on oeis4.)