A212375 - OEIS

%I #17 Sep 08 2022 08:46:02

%S 3,5,7,11,13,19,29,37,43,53,59,61,67,73,79,83,97,101,103,107,109,131,

%T 139,149,151,157,163,173,179,181,193,197,199,211,227,229,241,251,269,

%U 271,277,283,293,307,313,317,331,337,347,349,367,373,379,389,397

%N Primes p such that x^18 = 2 has no solution mod p.

%C Complement of A049550 relative to A000040.

%C This sequence is not the same as A040993. First disagreement at index 59: a(59)=433, A040993(59)=443.

%H Bruno Berselli, <a href="/A212375/b212375.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 18, #], Mod[2, #]] &]

%t ok[p_]:= Reduce[Mod[x^18 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* _Vincenzo Librandi_, Sep 20 2012  *)

%o (Magma) [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^18 ne 2}];

%o (Magma) [p: p in PrimesUpTo(400) | not exists{x : x in ResidueClassRing(p) | x^18 eq 2} ]; // _Vincenzo Librandi_, Sep 20 2012

%Y Cf. A000040, A049550.

%Y Cf. A040993.

%K nonn,easy

%O 1,1

%A _Bruno Berselli_, Sep 13 2012