A059643 - OEIS

%I #15 Sep 08 2022 08:45:03

%S 7,13,19,37,61,67,73,79,97,103,139,151,163,181,191,193,199,211,229,

%T 241,271,313,331,337,349,367,373,379,409,419,421,457,463,487,523,541,

%U 547,571,577,607,613,619,631,647,661,673,709,751,757,761,769,787,823,829

%N Primes p such that x^57 = 2 has no solution mod p.

%C Complement of A049589 relative to A000040.

%H Vincenzo Librandi, <a href="/A059643/b059643.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^57 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) [p: p in PrimesUpTo(900) | not exists{x: x in ResidueClassRing(p) | x^57 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012

%o (PARI)

%o N=10^4;  default(primelimit,N);

%o ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }

%o forprime(p=2,N, if (! ok(p,2,57),print1(p,", ")));

%o /* _Joerg Arndt_, Sep 21 2012 */

%Y Cf. A000040, A049589.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001