A059642 - OEIS

%I #11 Sep 08 2022 08:45:03

%S 11,23,31,41,61,67,71,89,101,131,181,191,199,211,271,281,311,331,353,

%T 397,401,419,421,461,463,491,521,541,601,617,631,661,683,691,701,727,

%U 751,761,811,821,859,881,941,947,991,1021,1031,1051,1061,1091,1123

%N Primes p such that x^55 = 2 has no solution mod p.

%C Complement of A049587 relative to A000040.

%H Vincenzo Librandi, <a href="/A059642/b059642.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^55 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) [p: p in PrimesUpTo(1150) | not exists{x: x in ResidueClassRing(p) | x^55 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,2,55),print1(p,", ")));

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

%Y Cf. A000040, A049587.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001