A090686 Primes of the form 6n^2 - 1.

5, 23, 53, 149, 293, 383, 599, 863, 1013, 1733, 2399, 2903, 4373, 4703, 5399, 6143, 7349, 8663, 11093, 12149, 16223, 18149, 20183, 21599, 23063, 23813, 25349, 27743, 29399, 31973, 33749, 35573, 40343, 41333, 45413, 51893, 56453, 59999, 62423

Offset: 1

Author

Cino Hilliard, Dec 18 2003

Keywords

• easy
• nonn

Comments

Subset of A007528. The values of n for which 6*n^2 - 1 is prime are 1, 2, 3, 5, 7, 8, 10, 12, 13, 17, 20, 22, 27, 28, 30, 32, 35, 38, 43, 45, 52, 55, 58, 60, 62, 63, 65, 68, 70, 73, 75, 77, 82, 83, 87, 93, 97, 100, ... - Jonathan Vos Post, Aug 27 2006

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A007528, A090687.

Programs

Magma

[a: n in [0..500] | IsPrime(a) where a is 6*n^2-1]; // Vincenzo Librandi, Dec 05 2011

Mathematica

lst={};Do[p=6*n^2-1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,3*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)
Select[Table[6n^2-1,{n,0,700}],PrimeQ] (* Vincenzo Librandi, Dec 05 2011 *)

PARI

mx2pmp(n) = { for(x=1,n, y = 6*x^2-1; if(isprime(y),print1(y",")) ) }

Extensions

Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Apr 14 2008