A125649 Smallest odd prime base q such that p^8 divides q^(p-1) - 1, where p = prime(n).

257, 13121, 3124999, 3376853, 174625993, 533810141, 16048035481, 3620189879, 982740799, 547344139109, 497929938133, 1105109875657, 15682480615619, 1391016035411, 83209719751, 84224951222611, 165554755409789, 254747341131683, 701000310909907, 317304132615017

Offset: 1

Author

Alexander Adamchuk, Nov 29 2006

Keywords

• nonn

Links

• W. Keller and J. Richstein Fermat quotients that are divisible by p.

Crossrefs

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

Programs

Mathematica

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 *)

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

Extensions

More terms from Ryan Propper, Apr 01 2007

More terms from Max Alekseyev, May 30 2007