login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Smallest odd prime base q such that p^6 divides q^(p-1) - 1, where p = Prime[n].
11

%I #6 Mar 31 2012 13:20:34

%S 193,1459,14557,152617,2120879,7654109,24527681,2342959,90603883,

%T 1657641497,40373093,2175429661,1614357949,119612113,14635471219,

%U 2816276179,15591204869,1006953931,7726467079,48931161299,54908441659,41985419521,583493688221,200335697059,96891225583,50303508131,129847013561,362253784469,625810253147,195406393583

%N Smallest odd prime base q such that p^6 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>.

%o (PARI) { a(n) = local(p,x,y); if(n==1,return(193)); p=prime(n); x=znprimroot(p^6)^(p^5); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^6);y ) )[1] } - _Max Alekseyev_, May 30 2007

%Y Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125648, A125649.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 29 2006

%E More terms from _Max Alekseyev_, May 30 2007