A212376 - OEIS

%I #19 Sep 08 2022 08:46:02

%S 3,5,7,11,13,17,19,29,37,41,43,53,59,61,67,73,79,83,97,101,103,107,

%T 109,113,131,137,139,149,151,157,163,173,179,181,193,197,199,211,227,

%U 229,241,251,269,271,277,281,283,293,307,313,317,331,337,347,349,353,367

%N Primes p such that x^48 = 2 has no solution mod p.

%C Complement of A049580 relative to A000040.

%C This sequence is not the same as A059362. First disagreement at index 162: a(162)=1217, A059362(162)=1229.

%H Bruno Berselli, <a href="/A212376/b212376.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] &]

%t ok[p_] := Reduce[Mod[x^48 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[75]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^48 ne 2}];

%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,2,48),print1(p,", ")));

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

%Y Cf. A000040, A049580.

%Y Cf. A059362.

%K nonn,easy

%O 1,1

%A _Bruno Berselli_, Sep 14 2012