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

0,5

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for sequences related to factorial numbers.

Formula

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

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

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

Example

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

Mathematica

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

Prog

(Haskell)
import Data.List (nub, sort)
a137580 = length . nub . show . a000142
-- Reinhard Zumkeller, Apr 08 2012
(PARI) A137580(n)=#Set(digits(n!)) \\ M. F. Hasler, May 04 2015

Crossrefs

Cf. A137577, A137578.

Cf. A034886.

Sequence in context: A049206 A194247 A084767 * A340068 A196369 A245710

Adjacent sequences: A137577 A137578 A137579 * A137581 A137582 A137583

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 27 2008

Status

approved