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%I #22 Sep 08 2022 08:45:07
%S 1,2,15,21,29,39,42,53,57,77,81,92,117,123,131,147,149,153,167,168,
%T 200,204,207,233,249,251,252,275,278,314,317,326,357,372,378,380,410,
%U 422,434,438,440,462,467,468,498,516,546,585,587,596,608,615,621,636
%N Numbers n such that 1 + n + n^s is a prime, s = 7.
%C 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).
%H T. D. Noe, <a href="/A075722/b075722.txt">Table of n, a(n) for n=1..1000</a>
%e 15 is OK because at s=7, n=15, n_s = 1 + n + n^s = 170859391 is a prime.
%t Select[Range[1000], PrimeQ[1 + # + #^7] &] (* _Vincenzo Librandi_, Jul 28 2014 *)
%o (Magma) [n: n in [0..1000] | IsPrime(s) where s is 1+n+n^7]; // _Vincenzo Librandi_, Jul 28 2014
%o (PARI) for(n=1,10^3,if(isprime(n^7+n+1),print1(n,", "))) \\ _Derek Orr_, Feb 07 2015
%Y Cf. A002384, A075720, A075723.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Oct 03 2002
%E More terms from _Ralf Stephan_, Apr 05 2003