A136692 Final nonzero digit of n! in base 5.

1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1, 1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 3, 3, 1, 3, 2, 4, 4, 3, 4, 1, 3, 3, 1, 3, 2, 3, 3, 1, 3, 2, 1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1

Offset

0,3

Links

Table of n, a(n) for n=0..99.

Formula

a(n) = (n!/A243757(n)) mod 5. - Ridouane Oudra, Sep 27 2024

Example

6! = 720 decimal = 10340 quinary, so a(6) = 4.

Mathematica

Table[Module[{sp=Split[IntegerDigits[n!, 5]]}, If[sp[[-1, -1]]==0, sp[[-2, -1]], sp[[-1, -1]]]], {n, 0, 100}] (* Harvey P. Dale, Oct 26 2016 *)

Prog

(PARI) a(n)={my(v=[1, 1, 2, 1, 4, 4, 4, 3, 4, 1]); if(n==0, 1, lift(prod(k=0, logint(n, 5), Mod(v[1 + n\5^k % 10], 5))))} \\ Andrew Howroyd, Sep 27 2024

Crossrefs

Cf. A000142, A136690, A136691, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

Cf. A243757.

Sequence in context: A345674 A296337 A308432 * A368673 A219194 A234306

Adjacent sequences: A136689 A136690 A136691 * A136693 A136694 A136695

Keyword

base,easy,nonn

Author

Carl R. White, Jan 16 2008

Status

approved