This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049545 #18 Jul 20 2025 10:12:42
%S A049545 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,59,61,67,71,73,83,89,97,101,
%T A049545 103,107,109,113,127,137,139,149,151,163,167,173,179,181,191,193,197,
%U A049545 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293
%N A049545 Primes p such that x^13 = 2 has a solution mod p.
%C A049545 Complement of A059245 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%H A049545 R. J. Mathar, <a href="/A049545/b049545.txt">Table of n, a(n) for n = 1..1000</a>
%H A049545 <a href="/index/Pri#smp">Index entries for related sequences</a>
%e A049545 0^13 == 2 (mod 2). 2^13 == 2 (mod 3). 2^13 == 2 (mod 5). 2^13 == 2 (mod 7). 7^13 == 2 (mod 11). 2^13 == 2 (mod 13). 15^13 == 2 (mod 17). 14^13 == 2 (mod 19). 18^13 == 2 (mod 23). 14^13 == 2 (mod 29). 4^13 == 2 (mod 31). 20^13 == 2 (mod 37). 36^13 == 2 (mod 41). 22^13 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025
%t A049545 ok[p_]:= Reduce[Mod[x^13- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)
%o A049545 (Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^13 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012
%Y A049545 Cf. A000040, A059245.
%K A049545 nonn,easy
%O A049545 1,1
%A A049545 _N. J. A. Sloane_