A163512 Primes of the form (1 + k + k^3)/3.

23, 337, 2293, 3557, 9941, 21347, 39233, 87403, 251221, 333367, 895253, 1080647, 1217473, 1696207, 2076563, 2626933, 2999707, 4493837, 6203297, 6857033, 8045953, 8299127, 8821297, 11442817, 13807361, 14538187, 17298497, 21333467

Offset

1,1

Comments

k must be congruent to 1 (mod 3) for (k^3 + k + 1)/3 to be an integer. - Michael B. Porter, Apr 07 2010

Links

J. Mulder, Table of n, a(n) for n = 1..40000

Example

(1 + 4 + 4^3)/3 = 23.

Mathematica

f[n_]:=(1+n+n^3)/3; lst={}; Do[If[PrimeQ[f[n]], AppendTo[lst, f[n]]], {n, 7!}]; lst
Select[Table[(n^3+n+1)/3, {n, 400}], PrimeQ] (* Harvey P. Dale, Aug 28 2012 *)

Prog

(PARI) for(n=0, 200, m=3*n+1; if(isprime((m^3+m+1)/3), print((m^3+m+1)/3))) \\ Michael B. Porter, Apr 07 2010

Crossrefs

Sequence in context: A220648 A243422 A028110 * A028059 A299710 A028055

Adjacent sequences: A163509 A163510 A163511 * A163513 A163514 A163515

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 29 2009

Status

approved