A193051 Primes p such that 12*p^2-1 and 16*p^3-1 are also primes.

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

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