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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

%I

%S 157181,244603,276371,491371,1266631,1954531,2511911,2866837,4070201,

%T 4285381,4311037,4682297,4826897,5200123,5531353,5644267,6195731,

%U 6581591,7738001,8290837,8606053,8760107,8770547,9309907,9521453,10562147,11142413,11532163,12206021,12631111

%N 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.

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

%H Pierre CAMI, <a href="/A245681/b245681.txt">Table of n, a(n) for n = 1..243</a>

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

%t 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 *)

%o (PFGW & SCRIPT)

%o SCRIPT

%o DIM i

%o DIM j,0

%o DIM k

%o DIM n,0

%o DIMS t

%o OPENFILEOUT myf,a(n).txt

%o LABEL loop1

%o SET j,j+1

%o SET n,p(j)

%o SETS t,%d\ ;n

%o SET i,24*n^3-1

%o PRP i,t

%o IF ISPRP THEN GOTO a

%o GOTO loop1

%o LABEL a

%o SET k,24*i^3-1

%o PRP k,t

%o IF ISPRP THEN GOTO b

%o GOTO loop1

%o LABEL b

%o SET i,24*k^3-1

%o PRP i,t

%o IF ISPRP THEN GOTO c

%o GOTO loop1

%o LABEL c

%o WRITE myf,t

%o GOTO loop1

%o (PARI)

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

%o 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

%Y Cf. A245640.

%K nonn

%O 1,1

%A _Pierre CAMI_, Jul 29 2014

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)