A165683 Primes of form 3*p*(p-1)+1 with p also a prime.

7, 19, 61, 127, 331, 2437, 2791, 5419, 8269, 10267, 13267, 23497, 35317, 55897, 73477, 89269, 115837, 170647, 292969, 360187, 372769, 452797, 603457, 812761, 895987, 929077, 976411, 997057, 1074607, 1125469, 1253887, 1372957, 1609669, 1653919

Offset

1,1

Links

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

Formula

a(n) = x^3-(x-1)^3 where x = A165682(n).

Example

a(3)= 61=3*5*(5-1)+1 generated by p=3. a(4)=127=3*7*(7-1)+1 generated by p=7. a(5)=331=3*11*(11-1)+1.

Mathematica

Select[Table[3 p (p - 1) + 1, {p, Prime[Range[100]]}], PrimeQ] (* Vincenzo Librandi, Sep 13 2013 *)

Prog

(Magma) [a: p in PrimesUpTo(1000) | IsPrime(a) where a is 3*p*(p-1)+1]; // Vincenzo Librandi, Sep 13 2013 *

Crossrefs

Cf. A165681, A165682.

Sequence in context: A155226 A229442 A179406 * A092359 A259797 A155338

Adjacent sequences: A165680 A165681 A165682 * A165684 A165685 A165686

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 24 2009

Extensions

7 and 19 inserted by R. J. Mathar, Sep 26 2009

Status

approved