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%I #25 Sep 08 2022 08:45:02
%S 53,79,131,157,313,443,521,547,599,677,859,911,937,1093,1171,1223,
%T 1249,1301,1327,1483,1613,1847,1873,1951,2003,2029,2081,2237,2341,
%U 2393,2549,2731,2861,2887,2939,3121,3251,3329,3407,3433,3511,3719,3797,3823,4057
%N Primes p such that x^13 = 2 has no solution mod p.
%C Complement of A049545 relative to A000040.
%C Presumably this is the same as Primes congruent to 1 mod 13. - _N. J. A. Sloane_, Jul 11 2008
%C The smallest counterexample is 4421: 4421 == 1 (mod 13), but 162^13 == 2 (mod 4421), therefore this prime is not in the sequence. - _Bruno Berselli_, Sep 12 2012
%H Vincenzo Librandi, <a href="/A059245/b059245.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Prime[Range[PrimePi[5000]]], ! MemberQ[PowerMod[Range[#], 13, #], Mod[2, #]] &] (* _T. D. Noe_, Sep 12 2012 *)
%t ok[p_]:= Reduce[Mod[x^13 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[600]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(4500) | forall{x: x in ResidueClassRing(p) | x^13 ne 2}]; // _Bruno Berselli_, Sep 12 2012
%Y Cf. A000040, A049545, A268753.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 21 2001
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