A119264 Primes of the form k^6 + k^2 + 1.

3, 739, 2986129, 11390851, 191103553, 387421219, 1291469059, 2176783633, 8303767651, 24794914213, 34296450499, 646990192099, 782757798913, 2194972636933, 3462826006819, 14412774469393, 27752076894853

Offset: 1

Author

Jonathan Vos Post, Jul 23 2006

Keywords

• easy
• nonn
• less

Comments

The numbers k such that k^6 + k^2 + 1 is prime begin 1, 3, 12, 15, 24, 27, 33, 36, 45, 54, 57, 93, 96, 114, 123, 156, 174, 177, 210, ...; other than 1, each is divisible by 3.

Examples

			a(1) = 1^6 + 1^2 + 1 = 3 is prime.
a(2) = 3^6 + 3^2 + 1 = 739 is prime.
a(3) = 12^6 + 12^2 + 1 = 2986129 is prime.
a(4) = 15^6 + 15^2 + 1 = 11390851 is prime.
		

Crossrefs

Cf. A000040, A120479, A120480.

Programs

Magma

[a: n in [0..250]|IsPrime(a) where a is n^6+n^2+1] // Vincenzo Librandi, Dec 22 2010

Mathematica

Select[Table[n^6+n^2+1,{n,200}],PrimeQ] (* Harvey P. Dale, Oct 17 2019 *)

Formula

a(n) = A000040 INTERSECTION {n^6 + n^2 + 1}.

Extensions

a(1) corrected by Vincenzo Librandi, Dec 22 2010