

A049408


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


14



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
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OFFSET

1,2


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.


LINKS

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


EXAMPLE

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


MATHEMATICA

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


PROG

(PARI) for(n=1, 1000, if(isprime(1+n+n^4), print1(n", ")))
(MAGMA) [n: n in [0..1000]  IsPrime(s) where s is 1+n+n^4]; // Vincenzo Librandi, Jul 28 2014


CROSSREFS

Cf. A002384, A075723, A049407.
Sequence in context: A281902 A153143 A075724 * A342733 A138970 A168550
Adjacent sequences: A049405 A049406 A049407 * A049409 A049410 A049411


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



