A283149 Largest k such that (p-1)! == -1 (mod p^k), where p = prime(n).

1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1

Offset

1,3

Comments

a(n) > 1 iff A002068(n) = 0, i.e., iff p is a Wilson prime (A007540).

Is a(n) < 3 for all n?

Links

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

Maple

f:= proc(n) local p;
  p:= ithprime(n);
  padic:-ordp((p-1)!+1, p)
end proc:
map(f, [$1..200]); # Robert Israel, Apr 29 2021

Mathematica

Table[With[{p = Prime@ n}, SelectFirst[Reverse@ Range@ 10, Mod[(p - 1)!, #] == # - 1 &[p^#] &]], {n, 105}] (* Michael De Vlieger, Aug 20 2017 *)

Prog

(PARI) a(n) = my(p=prime(n), k=1); while(Mod((p-1)!, p^k)==-1, k++); k-1

Crossrefs

Cf. A002068, A007540.

Sequence in context: A321765 A328310 A136673 * A097588 A183017 A183014

Adjacent sequences: A283146 A283147 A283148 * A283150 A283151 A283152

Keyword

nonn

Author

Felix Fröhlich, Mar 01 2017

Extensions

More terms from Antti Karttunen, Aug 20 2017

Status

approved