Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #25 Sep 08 2022 08:45:02
%S 107,743,1061,1697,2333,2969,3181,3499,3923,4241,4877,5407,6043,6361,
%T 6679,6997,7103,7951,8269,8693,9011,9859,10177,10601,11131,12721,
%U 13463,13781,14629,14947,15053,15583,15901,16007,17491,17597,18127,18233
%N Primes p such that x^53 = 2 has no solution mod p.
%C Complement of A049585 relative to A000040.
%C Presumably this is also Primes congruent to 1 mod 53 (A212377). - _N. J. A. Sloane_, Jul 11 2008
%C Not so. The smallest counterexample is the prime 91373: 91373 == 1 (mod 53), but 2246^53 == 2 (mod 91373), therefore this prime is not in the sequence. - _Bruno Berselli_, Sep 20 2012
%H Vincenzo Librandi, <a href="/A059258/b059258.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_] := Reduce[Mod[x^53 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^53 eq 2}]; // _Vincenzo Librandi_, Sep 20 2012
%Y Cf. A000040, A049585, A212377.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 23 2001