A245674 Prime numbers P such that 8*P^2-1 and 8*(8*P^2-1)^2-1 are also prime numbers.

2, 79, 107, 173, 257, 359, 383, 523, 593, 971, 1493, 1811, 1867, 2273, 2357, 3187, 4111, 4723, 6389, 7607, 8101, 8699, 9473, 11027, 12157, 12227, 15017, 16301, 16987, 18797, 19801, 19913, 20071, 20323, 21313, 22003, 22307, 23203, 24229, 24733, 24859, 24943

Offset

1,1

Comments

Subsequence of A245639.

For P < 150000000 in this sequence, 8*(8*(8*P^2)^2-1)^2-1)^2-1 is composite.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

2 is prime, 8*2^2-1=31 is prime, 8*31^2-1=7687 is prime, so 2 is in the sequence.

Mathematica

f[n_]:=8 n^2 - 1; Select[Prime[Range[3000]], PrimeQ[f[#]]&&PrimeQ[f[f[#]]]&] (* Vincenzo Librandi, Sep 08 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i
DIM j, 0
DIM n, 0
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET j, j+1
SETS t, %d\ ; p(j)
SET i, 8*p(j)^2-1
PRP i, t
IF ISPRP THEN GOTO a
GOTO loop1
LABEL a
SET i, 8*i^2-1
PRP i, t
IF ISPRP THEN GOTO b
GOTO loop1
LABEL b
WRITE myf, t
GOTO loop1
(PARI)
f(x) = 8*x^2-1;
forprime(p=1, 10^8, if(ispseudoprime(f(p)) && ispseudoprime(f(f(p))), print1(p, ", "))) \\ Derek Orr, Jul 29 2014
(Magma) [p: p in PrimesUpTo(25000)| IsPrime(8*p^2-1)and IsPrime(512*p^4-128*p^2+7)]; // Vincenzo Librandi, Sep 08 2014

Crossrefs

Cf. A245639.

Sequence in context: A008273 A231240 A197101 * A342979 A166052 A045484

Adjacent sequences: A245671 A245672 A245673 * A245675 A245676 A245677

Keyword

nonn,easy

Author

Pierre CAMI, Jul 29 2014

Status

approved