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.

A042966 Primes p such that x^7 = 2 has a solution mod p.

This page as a plain text file.
%I A042966 #41 Sep 08 2022 08:44:55
%S A042966 2,3,5,7,11,13,17,19,23,31,37,41,47,53,59,61,67,73,79,83,89,97,101,
%T A042966 103,107,109,131,137,139,149,151,157,163,167,173,179,181,191,193,199,
%U A042966 223,227,229,233,241,251,257,263,269,271,277,283,293,307,311,313,317,331
%N A042966 Primes p such that x^7 = 2 has a solution mod p.
%C A042966 Coincides with sequence of "primes p such that x^49 = 2 has a solution mod p" for first 572 terms, then diverges.
%C A042966 Complement of A042967 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%C A042966 a(98) = 631 is the first such prime that is congruent to 1 (mod 7). - _Georg Fischer_, Jan 06 2022
%H A042966 T. D. Noe, <a href="/A042966/b042966.txt">Table of n, a(n) for n = 1..1000</a>
%H A042966 <a href="/index/Pri#smp">Index entries for related sequences</a>
%t A042966 ok[p_]:= Reduce[Mod[x^7 - 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)
%o A042966 (Magma) [p: p in PrimesUpTo(400) | exists{x: x in ResidueClassRing(p) | x^7 eq 2}]; // _Bruno Berselli_, Sep 12 2012
%Y A042966 Cf. A000040, A042967.
%Y A042966 For primes p such that x^m == 2 mod p has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...
%K A042966 nonn,easy
%O A042966 1,1
%A A042966 _N. J. A. Sloane_