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%I #17 Sep 08 2022 08:45:02
%S 367,733,977,1709,1831,2441,3539,4027,4271,4637,4759,5003,5857,6101,
%T 6833,7321,7687,8053,8297,8419,8663,9029,9151,9883,10859,12323,12689,
%U 13177,13421,14153,14519,15373,15739,16349,17203,17569,18301,18911
%N Primes p such that x^61 = 2 has no solution mod p.
%C Presumably this is also Primes congruent to 1 mod 61 (A212378). - _N. J. A. Sloane_, Jul 11 2008
%C Complement of A216884 relative to A000040. - _Vincenzo Librandi_, Sep 20 2012
%C Regarding the first comment, the smallest counterexample is the prime 34039: 34039 == 1 (mod 61), but 1155^61 == 2 (mod 34039), therefore this prime is not in the sequence. - _Bruno Berselli_, Sep 20 2012
%H Vincenzo Librandi, <a href="/A059230/b059230.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_]:= Reduce[Mod[x^61 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[5000]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(19000) | forall{x: x in ResidueClassRing(p) | x^61 ne 2} ]; // _Vincenzo Librandi_, Sep 20 2012
%Y Cf. A000040, A058853, A212378.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 20 2001
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