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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
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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jul 29 2014
STATUS
approved

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Last modified June 21 06:38 EDT 2024. Contains 373540 sequences. (Running on oeis4.)