A075722 Numbers n such that 1 + n + n^s is a prime, s = 7.

1, 2, 15, 21, 29, 39, 42, 53, 57, 77, 81, 92, 117, 123, 131, 147, 149, 153, 167, 168, 200, 204, 207, 233, 249, 251, 252, 275, 278, 314, 317, 326, 357, 372, 378, 380, 410, 422, 434, 438, 440, 462, 467, 468, 498, 516, 546, 585, 587, 596, 608, 615, 621, 636

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=7 and find several first n's making n_s a prime (or a probable prime).

Examples

			15 is OK because at s=7, n=15, n_s = 1 + n + n^s = 170859391 is a prime.
		

Links

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

Crossrefs

Cf. A002384, A075720, A075723.

Programs

Magma

[n: n in [0..1000] | IsPrime(s) where s is 1+n+n^7]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[1000], PrimeQ[1 + # + #^7] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

for(n=1,10^3,if(isprime(n^7+n+1),print1(n,", "))) \\ Derek Orr, Feb 07 2015

Extensions

More terms from Ralf Stephan, Apr 05 2003