This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A075723 #20 Sep 08 2022 08:45:07 %S A075723 1,2,3,6,8,15,17,29,30,32,45,48,59,72,74,80,87,128,141,153,155,156, %T A075723 158,176,182,191,197,210,216,230,273,284,293,305,314,356,366,380,384, %U A075723 399,402,407,408,410,413,420,435,443,447,450,473,479,497 %N A075723 Numbers n such that 1 + n + n^6 is a prime. %C A075723 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=6 and find several first n's making n_s a prime (or a probable prime). %H A075723 T. D. Noe, <a href="/A075723/b075723.txt">Table of n, a(n) for n = 1..1000</a> %e A075723 15 is OK because at s=6, n=15, n_s = 1 + n + n^s = 11390641 is a prime. %t A075723 Select[Range[500], PrimeQ[1 + # + #^6] &] (* _Vincenzo Librandi_, Jul 28 2014 *) %o A075723 (Magma) [n: n in [0..500] | IsPrime(s) where s is 1+n+n^6]; // _Vincenzo Librandi_, Jul 28 2014 %o A075723 (PARI) for(n=1,10^3,if(isprime(n^6+n+1),print1(n,", "))) \\ _Derek Orr_, Feb 07 2015 %Y A075723 Cf. A002384, A049407, A049408. %K A075723 nonn,easy %O A075723 1,2 %A A075723 _Zak Seidov_, Oct 03 2002