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.

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

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