%I #17 Sep 08 2022 08:44:58

%S 2,7,23,31,47,71,73,89,103,113,127,151,167,191,199,223,233,239,257,

%T 263,271,281,311,337,353,359,367,383,431,439,463,479,487,503,577,593,

%U 601,607,617,631,647,719,727,743,751,823,839,863,881,887,919,967,983,991

%N Primes p such that x^52 = 2 has a solution mod p.

%C Complement of A059641 relative to A000040. - _Vincenzo Librandi_, Sep 14 2012

%H R. J. Mathar, <a href="/A049584/b049584.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#smp">Index entries for related sequences</a>

%t ok[p_]:= Reduce[Mod[x^52 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 14 2012 *)

%o (Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^52 eq 2}]; // _Vincenzo Librandi_, Sep 14 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,2,52),print1(p,", ")));

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

%Y Cf. A000040, A059641.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_