A040991 - OEIS

%I #9 Sep 08 2022 08:44:53

%S 31,41,61,101,131,181,191,211,241,251,281,311,401,421,431,491,521,541,

%T 571,601,631,641,661,751,811,821,881,911,941,971,991,1021,1031,1051,

%U 1061,1091,1151,1171,1181,1201,1231,1291,1301,1321,1361,1381,1451,1471,1481

%N Primes p such that x^5 = 23 has no solution mod p.

%C Complement of A040990 relative to A000040. - _Vincenzo Librandi_, Sep 19 2012

%H Vincenzo Librandi, <a href="/A040991/b040991.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^5 - 23, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 19 2012 *)

%o (Magma) [p: p in PrimesUpTo(1500) | not exists{x : x in ResidueClassRing(p) | x^5 eq 23} ]; // _Vincenzo Librandi_, Sep 19 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.