A075719 1+n+n^s is a prime, s=10.

1, 3, 8, 21, 23, 26, 33, 36, 38, 45, 51, 57, 69, 71, 78, 92, 107, 117, 149, 156, 170, 176, 179, 195, 209, 216, 219, 224, 261, 293, 321, 341, 359, 374, 378, 386, 390, 404, 410, 413, 420, 474, 492, 507, 516, 546, 569, 572, 582, 621, 632, 683, 767, 783, 789, 809

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 at n=1, n_s=3 is a prime for any s. So it is interesting to consider only the cases of s =/= 5,8,11,14,17,20,... and n>1. Here i consider the case s=10 and find several first n's making n_s a prime (or a probable prime).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3300

Example

3 is OK because at s=10, n=3, n_s=1+n+n^s=59053 is a prime.

Mathematica

Select[Range[1000], PrimeQ[1 + # + #^10] &] (* Vincenzo Librandi, Jul 28 2014 *)

Prog

(PARI) for(n=1, 1000, if(isprime(1+n+n^10), print1(n", ")))
(Magma) [n: n in [0..1000] | IsPrime(s) where s is 1+n+n^10]; // Vincenzo Librandi, Jul 28 2014

Crossrefs

Cf. A002384, A075718, A075720.

Sequence in context: A291176 A066212 A171437 * A245205 A101643 A334136

Adjacent sequences: A075716 A075717 A075718 * A075720 A075721 A075722

Keyword

nonn,easy

Author

Zak Seidov, Oct 03 2002

Extensions

More terms from Ralf Stephan, Apr 05 2003

Status

approved