A137580 Number of distinct digits in decimal representation of n!.

1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 6, 5, 6, 7, 5, 9, 8, 8, 9, 7, 7, 10, 9, 8, 9, 10, 8, 9, 9, 10, 9, 10, 10, 10, 10, 10, 9, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 0

Author

Reinhard Zumkeller, Jan 27 2008

Keywords

• nonn
• base

Examples

			n=12: 12! = 479001600 => a(12) = #{0,1,4,6,7,9} = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A137577, A137578.

Cf. A034886.

Programs

Haskell

import Data.List (nub, sort)
a137580 = length . nub . show . a000142
-- Reinhard Zumkeller, Apr 08 2012

Mathematica

Map[Length[Union[IntegerDigits[#]]] &, Table[n!, {n, 0, 79}]] (* Geoffrey Critzer, May 25 2013 *)

PARI

A137580(n)=#Set(digits(n!)) \\ M. F. Hasler, May 04 2015

Formula

a(n) = A043537(A000142(n)).

a(n) < 10 iff A137579(n) = 0.

a(A182049(n)) < 10. - Reinhard Zumkeller, Apr 08 2012