A136695 Final nonzero digit of n! in base 8.

1, 1, 2, 6, 3, 7, 2, 6, 6, 6, 4, 4, 6, 6, 4, 4, 3, 3, 6, 2, 5, 1, 6, 2, 6, 6, 4, 4, 6, 6, 4, 4, 6, 6, 4, 4, 2, 2, 4, 4, 4, 4, 1, 3, 4, 4, 3, 5, 6, 6, 4, 4, 2, 2, 4, 4, 4, 4, 3, 1, 4, 4, 5, 3, 3, 3, 6, 2, 1, 5, 6, 2, 2, 2, 4, 4, 2, 2, 4, 4, 5, 5, 2, 6, 3, 7, 2, 6, 2, 2, 4, 4, 2, 2, 4, 4, 6, 6, 4, 4

Offset: 0

Author

Carl R. White, Jan 16 2008

Keywords

• base
• easy
• nonn

Examples

			6! = 720 decimal = 1320 octal, so a(6) = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

Cf. A011371, A049606.

Programs

Maple

P:= 1: E:= 0: a[0]:= 1:
for n from 1 to 100 do
  v:= padic:-ordp(n,2);
  P:= P*(n/2^v) mod 8;
  E:= E + v;
  if E mod 3 = 0 then a[n]:= P
  elif E mod 3 = 1 then a[n]:= 2*(P mod 4)
  else a[n]:= 4
  fi
od:
seq(a[n],n=0..100); # Robert Israel, Sep 26 2018

Mathematica

Table[IntegerDigits[FromDigits[Reverse[IntegerDigits[n!,8]]]][[1]],{n,0,100}] (* Harvey P. Dale, Nov 29 2024 *)

Formula

From Robert Israel, Sep 26 2018: (Start)

If A011371(n) == 0 (mod 3) then a(n) = A049606(n) mod 8.

If A011371(n) == 1 (mod 3) then a(n) = 2*(A049606(n) mod 4).

If A011371(n) == 2 (mod 3) then a(n) = 4. (End)