A042966 - OEIS

%I #41 Sep 08 2022 08:44:55

%S 2,3,5,7,11,13,17,19,23,31,37,41,47,53,59,61,67,73,79,83,89,97,101,

%T 103,107,109,131,137,139,149,151,157,163,167,173,179,181,191,193,199,

%U 223,227,229,233,241,251,257,263,269,271,277,283,293,307,311,313,317,331

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

%C Coincides with sequence of "primes p such that x^49 = 2 has a solution mod p" for first 572 terms, then diverges.

%C Complement of A042967 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012

%C a(98) = 631 is the first such prime that is congruent to 1 (mod 7). - _Georg Fischer_, Jan 06 2022

%H T. D. Noe, <a href="/A042966/b042966.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#smp">Index entries for related sequences</a>

%t ok[p_]:= Reduce[Mod[x^7 - 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)

%o (Magma) [p: p in PrimesUpTo(400) | exists{x: x in ResidueClassRing(p) | x^7 eq 2}]; // _Bruno Berselli_, Sep 12 2012

%Y Cf. A000040, A042967.

%Y 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 nonn,easy

%O 1,1

%A _N. J. A. Sloane_