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A193051 Primes p such that 12*p^2-1 and 16*p^3-1 are also primes. 1
2, 3, 17, 29, 107, 167, 173, 599, 1667, 1889, 2129, 3407, 3539, 3797, 3863, 5189, 6779, 6983, 7529, 8849, 11399, 11519, 11657, 12227, 12437, 12809, 13217, 14153, 15227, 16223, 16607, 17609, 21683, 21863, 22193, 23789, 25127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that 3*(2p)^2-1 (see A089681) and 2*(2p)^3-1 are primes.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

For p=2, 2 is a prime number, 12*2^2-1=47 is a prime number and 16*2^3-1=127 is a prime number.

For p=3, 3 is a prime number, 12*3^2-1=109 is a prime number and 16*3^3-1=431 is a prime number.

MATHEMATICA

fQ[n_] := PrimeQ[12 n^2 - 1] && PrimeQ[16 n^3 - 1]; Select[ Prime@ Range@ 3000, fQ] (* Robert G. Wilson v, Aug 08 2011 *)

Select[Prime[Range[5000]], PrimeQ[12 #^2 - 1] && PrimeQ[16 #^3 - 1]&] (* Vincenzo Librandi, Apr 10 2013 *)

PROG

(MAGMA) [p: p in PrimesUpTo(26000)|IsPrime(12*p^2-1) and IsPrime(16*p^3-1)]; // Vincenzo Librandi, Apr 10 2013

CROSSREFS

Cf. A158463.

Sequence in context: A215303 A215280 A219559 * A217688 A263570 A029733

Adjacent sequences:  A193048 A193049 A193050 * A193052 A193053 A193054

KEYWORD

nonn,easy

AUTHOR

Juri-Stepan Gerasimov, Jul 15 2011

STATUS

approved

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Last modified December 9 09:37 EST 2021. Contains 349627 sequences. (Running on oeis4.)