A086358 Digital root of n!.

1, 1, 2, 6, 6, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,3

Comments

a(n) = 9 for n >= 6.

Links

Table of n, a(n) for n=0..105.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = A010888(n!) = fixed-point of A007953(n!). It equals n! modulo(9); at r = 0 use 9.

G.f.: (1 + x^2 + 4*x^3 - 3*x^5 + 6*x^6)/(1 - x). - Stefano Spezia, Jan 26 2023

Example

n = 5, 5 != 120, iteration list = {120,3}, a(5) = 3.

Mathematica

sud[x_] := Apply[Plus, DeleteCases[IntegerDigits[x], 0]]; Table[FixedPoint[sud, w!], {w, 1, 87}]

Crossrefs

Cf. A000142, A086353-A086361, A007953, A010888, A038194, A029898, A004152.

Sequence in context: A386926 A105815 A136696 * A004152 A071678 A316164

Adjacent sequences: A086355 A086356 A086357 * A086359 A086360 A086361

Keyword

nonn,base,easy

Author

Labos Elemer, Jul 21 2003

Extensions

a(0) = 1 prepended by Alois P. Heinz, Dec 05 2018

Status

approved