A125649 - OEIS

A125649

Smallest odd prime base q such that p^8 divides q^(p-1) - 1, where p = prime(n).

%I #13 Nov 17 2018 20:56:54

%S 257,13121,3124999,3376853,174625993,533810141,16048035481,3620189879,

%T 982740799,547344139109,497929938133,1105109875657,15682480615619,

%U 1391016035411,83209719751,84224951222611,165554755409789,254747341131683,701000310909907,317304132615017

%N Smallest odd prime base q such that p^8 divides q^(p-1) - 1, where p = prime(n).

%H W. Keller and J. Richstein <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>.

%t Do[p = Prime[n]; q = 2; While[PowerMod[q, p-1, p^8] != 1, q = NextPrime[q]]; Print[q], {n, 100}] (* _Ryan Propper_, Apr 01 2007 *)

%o (PARI) { a(n) = local(p,x,y); if(n==1,return(257)); p=prime(n); x=znprimroot(p^8)^(p^7); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^8);y ) )[1] } \\ _Max Alekseyev_, May 30 2007

%Y Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 29 2006

%E More terms from _Ryan Propper_, Apr 01 2007

%E More terms from _Max Alekseyev_, May 30 2007