A059667 Primes p such that x^49 = 2 has no solution mod p, but x^7 = 2 has a solution mod p.

4999, 6959, 7351, 11467, 15583, 16073, 20483, 21169, 21757, 30773, 35771, 37339, 38711, 41161, 45179, 46649, 48119, 51157, 51647, 57527, 58997, 64877, 75167, 75853, 80263, 83791, 84869, 85751, 86927, 93983, 95747, 105253, 110251, 115837

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..76

Mathematica

Select[Prime[Range[PrimePi[120000]]], ! MemberQ[PowerMod[Range[#], 49, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 7, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 21 2013 *)

Prog

(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, ", "))))
(PARI)
N=10^6;  default(primelimit, N);
ok(p, r, k1, k2)={
    if (  Mod(r, p)^((p-1)/gcd(k1, p-1))!=1, return(0) );
    if (  Mod(r, p)^((p-1)/gcd(k2, p-1))==1, return(0) );
    return(1);
}
forprime(p=2, N, if (ok(p, 2, 7, 7^2), print1(p, ", ")));
\\ Joerg Arndt, Sep 21 2012

Crossrefs

Cf. A042966, A042967, A070179 - A070188.

Sequence in context: A070001 A145540 A031840 * A106767 A157367 A200910

Adjacent sequences: A059664 A059665 A059666 * A059668 A059669 A059670

Keyword

nonn

Author

Klaus Brockhaus, Feb 04 2001

Status

approved