A136690 Final nonzero digit of n! in base 3.

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

Offset

0,3

Links

Kevin Ryde, Table of n, a(n) for n = 0..10000

Index entries for sequences that are fixed points of mappings

Formula

From David Radcliffe, Sep 03 2021: (Start)

a(n) = (n! / A060828(n)) mod 3;

a(n) = 1 + (A189672(n) mod 2);

a(6*n) = a(6*n+1) = a(2*n);

a(6*n+2) = 3 - a(2*n);

a(6*n+3) = a(6*n+4) = 3 - a(2*n+1);

a(6*n+5) = a(2*n+1).

(End)

a(n) = A008904(A127110(n)). - Michel Marcus, Sep 04 2021

From Kevin Ryde, Dec 03 2022: (Start)

a(n) = 1 if n written in base 9 has an even number of digits {2,3,4,6,7}; and otherwise a(n) = 2.

Fixed point of the morphism 1 -> 1,1,2,2,2,1,2,2,1; 2 -> 2,2,1,1,1,2,1,1,2; starting from 1.

(End)

Example

6! = 720 decimal = 222200 ternary, so a(6) = 2.

Mathematica

f[n_] := Mod[6 Times @@ (Rest[ FoldList[{1 + #1[[1]], #2! 2^(#1[[1]] #2)} &, {0, 0}, Reverse[ IntegerDigits[n, 3]]]]), 10][[2]]; # /. {0 -> 1} & /@ Mod[Table[f@n, {n, 0, 104}], 3] (* Robert G. Wilson v, Apr 17 2010 *)
fnzd[n_]:=Module[{sidn3=Split[IntegerDigits[n!, 3]]}, If[MemberQ[ Last[ sidn3], 0], sidn3[[-2, 1]], sidn3[[-1, 1]]]]; Array[fnzd, 110, 0] (* Harvey P. Dale, May 03 2018 *)

Prog

(PARI) a(n) = vecsum([bittest(220, b) |b<-digits(n, 9)])%2 + 1; \\ Kevin Ryde, Dec 03 2022

Crossrefs

Cf. A000142, A127110.

Other bases: A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

Sequence in context: A238421 A105154 A076447 * A144703 A276825 A270644

Adjacent sequences: A136687 A136688 A136689 * A136691 A136692 A136693

Keyword

base,easy,nonn

Author

Carl R. White, Jan 16 2008

Extensions

More terms from Robert G. Wilson v, Apr 17 2010

Status

approved