A075720 Numbers n such that n^9 + n + 1 is a prime.

1, 3, 9, 11, 14, 15, 18, 23, 38, 51, 66, 89, 95, 140, 170, 185, 186, 194, 239, 258, 294, 315, 345, 366, 384, 386, 393, 401, 404, 408, 429, 459, 485, 495, 506, 531, 573, 611, 614, 665, 675, 678, 680, 683, 695, 750, 771, 791, 849, 870, 879, 941, 954, 1016, 1086

Offset: 1

Author

Zak Seidov, Oct 03 2002

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 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=9 and find several first n's making n_s a prime (or a probable prime).

Examples

			9 is a member because at n=9, 1 + n + n^s = 387420499 is a prime.
		

Links

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

Crossrefs

Cf. A002384, A075719, A075722.

Programs

Magma

[n: n in [0..1500] | IsPrime(s) where s is 1+n+n^9]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[1500], PrimeQ[1 + # + #^9] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

for(n=1,10^3,if(isprime(n^9+n+1),print1(n,", "))) \\ Derek Orr, Feb 07 2015