A059667 - OEIS

%I #15 Sep 23 2013 03:09:28

%S 4999,6959,7351,11467,15583,16073,20483,21169,21757,30773,35771,37339,

%T 38711,41161,45179,46649,48119,51157,51647,57527,58997,64877,75167,

%U 75853,80263,83791,84869,85751,86927,93983,95747,105253,110251,115837

%N Primes p such that x^49 = 2 has no solution mod p, but x^7 = 2 has a solution mod p.

%H Vincenzo Librandi, <a href="/A059667/b059667.txt">Table of n, a(n) for n = 1..76</a>

%t Select[Prime[Range[PrimePi[120000]]], ! MemberQ[PowerMod[Range[#], 49, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 7, #], Mod[2, #]] &] (* _Vincenzo Librandi_, Sep 21 2013 *)

%o (PARI) forprime(p=2,116000,x=0; while(x<p&&x^7%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(7^2)%p!=2%p,y++); if(y==p,print1(p,","))))

%o (PARI)

%o N=10^6;  default(primelimit,N);

%o ok(p, r, k1, k2)={

%o     if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );

%o     if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );

%o     return(1);

%o }

%o forprime(p=2,N, if (ok(p,2,7,7^2),print1(p,", ")));

%o \\ _Joerg Arndt_, Sep 21 2012

%Y Cf. A042966, A042967, A070179 - A070188.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 04 2001