A125645 Smallest odd prime base q such that p^4 divides q^(p-1) - 1, where p = prime(n).

17, 163, 443, 3449, 45989, 239, 15541, 2819, 60793, 78017, 690143, 398023, 1977343, 574081, 1513367, 4388179, 3198427, 8065789, 3246107, 1353383, 5934307, 15631613, 2864371, 14754769, 15012733, 1358891, 32414783, 119551, 21860063, 11281097

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

Maple

f:= proc(n) local p, r, S, i, s, t;
  uses numtheory;
  p:= ithprime(n);
  r:= primroot(p^4);
  S:= sort([seq(r &^ (i*p^3) mod p^4, i=0..p-2)]);
  for i from 0 do
    for s in S do
      t:= i*p^4+s;
      if t::odd and isprime(t) then return t fi
  od od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Feb 12 2017

Prog

(PARI) { a(n) = local(p, x, y); if(n==1, return(17)); p=prime(n); x=znprimroot(p^4)^(p^3); vecsort( vector(p-1, i, y=lift(x^i); while(!isprime(y), y+=p^4); y ) )[1] } \\ Max Alekseyev, May 30 2007

Crossrefs

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125646, A125647, A125648, A125649.

Sequence in context: A164746 A198859 A160295 * A372965 A068518 A155664

Adjacent sequences: A125642 A125643 A125644 * A125646 A125647 A125648

Keyword

nonn,changed

Author

Alexander Adamchuk, Nov 29 2006

Extensions

More terms from Max Alekseyev, May 30 2007

Status

approved