A049408 Numbers k such that k^4 + k + 1 is prime.

1, 2, 5, 6, 9, 11, 12, 14, 24, 26, 32, 36, 44, 47, 60, 69, 72, 74, 77, 89, 90, 102, 107, 119, 126, 131, 146, 147, 159, 162, 170, 171, 186, 191, 197, 204, 206, 219, 239, 240, 252, 266, 284, 285, 290, 296, 300, 324, 347, 351, 362, 384, 426, 437, 459, 465, 470

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

For s = 5,8,11,14,17,20,..., n_s = 1 + n + n^s is always composite for any n > 1. Also for n=1, n_s=3 is a prime for any s. Here we consider the case s=4.

Examples

			26 is a term because at s=4, n=26, n_s = 1 + n + n^s = 457003 is a prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002384, A075723, A049407.

Programs

Magma

[n: n in [0..1000] | IsPrime(s) where s is 1+n+n^4]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[1000], PrimeQ[1 + # + #^4] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

for(n=1, 1000, if(isprime(1+n+n^4), print1(n",")))