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A245681 Prime numbers P such that Q=24*P^3-1 is prime, R=24*Q^3-1 is prime and S=24*R^3-1 is also prime. 1
157181, 244603, 276371, 491371, 1266631, 1954531, 2511911, 2866837, 4070201, 4285381, 4311037, 4682297, 4826897, 5200123, 5531353, 5644267, 6195731, 6581591, 7738001, 8290837, 8606053, 8760107, 8770547, 9309907, 9521453, 10562147, 11142413, 11532163, 12206021, 12631111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No prime number T=24*S^3-1 found for P < 160000000.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..243

MATHEMATICA

f[n_]:=24 n^3 - 1; Select[Prime[Range[13000000]], PrimeQ[f[#]]&&PrimeQ[f[f[#]]]&& PrimeQ[f[f[f[#]]]]&] (* Vincenzo Librandi, Sep 08 2014 *)

pnQ[n_]:=AllTrue[Rest[NestList[24#^3-1&, n, 3]], PrimeQ]; Select[ Prime[ Range[ 830000]], pnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 18 2015 *)

PROG

(PFGW & SCRIPT)

SCRIPT

DIM i

DIM j, 0

DIM k

DIM n, 0

DIMS t

OPENFILEOUT myf, a(n).txt

LABEL loop1

SET j, j+1

SET n, p(j)

SETS t, %d\ ; n

SET i, 24*n^3-1

PRP i, t

IF ISPRP THEN GOTO a

GOTO loop1

LABEL a

SET k, 24*i^3-1

PRP k, t

IF ISPRP THEN GOTO b

GOTO loop1

LABEL b

SET i, 24*k^3-1

PRP i, t

IF ISPRP THEN GOTO c

GOTO loop1

LABEL c

WRITE myf, t

GOTO loop1

(PARI)

f(x)=24*x^3-1

forprime(p=1, 10^8, if(ispseudoprime(f(p)) && ispseudoprime(f(f(p))) && ispseudoprime(f(f(f(p)))), print1(p, ", "))) \\ Derek Orr, Jul 29 2014

CROSSREFS

Cf. A245640.

Sequence in context: A114658 A274364 A258073 * A278862 A250595 A253311

Adjacent sequences:  A245678 A245679 A245680 * A245682 A245683 A245684

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jul 29 2014

STATUS

approved

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Last modified October 17 10:07 EDT 2019. Contains 328108 sequences. (Running on oeis4.)