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A212376 Primes p such that x^48 = 2 has no solution mod p.

%I A212376 #19 Sep 08 2022 08:46:02
%S A212376 3,5,7,11,13,17,19,29,37,41,43,53,59,61,67,73,79,83,97,101,103,107,
%T A212376 109,113,131,137,139,149,151,157,163,173,179,181,193,197,199,211,227,
%U A212376 229,241,251,269,271,277,281,283,293,307,313,317,331,337,347,349,353,367
%N A212376 Primes p such that x^48 = 2 has no solution mod p.
%C A212376 Complement of A049580 relative to A000040.
%C A212376 This sequence is not the same as A059362. First disagreement at index 162: a(162)=1217, A059362(162)=1229.
%H A212376 Bruno Berselli, <a href="/A212376/b212376.txt">Table of n, a(n) for n = 1..1000</a>
%t A212376 Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] &]
%t A212376 ok[p_] := Reduce[Mod[x^48 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[75]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)
%o A212376 (Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^48 ne 2}];
%o A212376 (PARI)
%o A212376 N=10^4;  default(primelimit,N);
%o A212376 ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
%o A212376 forprime(p=2,N, if (! ok(p,2,48),print1(p,", ")));
%o A212376 /* _Joerg Arndt_, Sep 21 2012 */
%Y A212376 Cf. A000040, A049580.
%Y A212376 Cf. A059362.
%K A212376 nonn,easy
%O A212376 1,1
%A A212376 _Bruno Berselli_, Sep 14 2012