cp's OEIS Frontend

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.

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

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