A120479 Primes of the form k^3 + k^2 + 1.

3, 13, 37, 151, 577, 811, 1453, 1873, 12697, 14401, 18253, 27901, 44101, 75853, 87121, 93151, 106033, 151687, 178753, 188443, 242173, 291853, 319057, 333271, 362953, 410701, 643453, 666073, 712891, 787153, 1040503, 1379953, 1742401, 1830733, 1875997, 1968751

Offset: 1

Author

Jonathan Vos Post, Jul 21 2006

Keywords

• easy
• nonn

Comments

Primes in A098547. - Michel Marcus, Jan 21 2015

Examples

			1^3 + 1^2 + 1 = 3 (prime), so 3 is in the sequence.
2^3 + 2^2 + 1 = 13 (prime), so 13 is in the sequence.
3^3 + 3^2 + 1 = 37 (prime), so 37 is in the sequence.
4^3 + 4^2 + 1 = 81 = 3^4, so 81 is not in the sequence.
5^3 + 5^2 + 1 = 151 (prime), so 151 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A119863 (corresponding k).

Cf. A000040, A098547.

Programs

Mathematica

Select[Table[n^3+n^2+1,{n,200}],PrimeQ] (* Harvey P. Dale, Oct 23 2020 *)

PARI

for(n=1,10^3,if(isprime(p=n^3+n^2+1),print1(p,", "))) \\ Derek Orr, Jan 21 2015

Formula

a(n) = A098547(A119863(n)). - Elmo R. Oliveira, Apr 20 2025