A204598 Least k such that n*k! contains every decimal digit at least once.

23, 17, 24, 24, 26, 25, 27, 24, 23, 23, 19, 17, 25, 25, 23, 23, 18, 26, 22, 17, 22, 20, 22, 18, 25, 29, 25, 28, 21, 24, 20, 23, 25, 16, 22, 23, 20, 25, 24, 24, 27, 24, 20, 19, 23, 22, 23, 27, 24, 26, 22, 24, 25, 25, 20, 20, 26, 23, 22, 25, 23, 19, 16, 17, 18

Offset

1,1

Comments

A property of this sequence: the arithmetic mean (1/x) *Sum_{k = 1..x} a(k) is very slowly decreasing when x increases. For example, s(100) = 22.5; s(1000) = 21.351; s(10000) = 20.2082; s(100000) = 19.24615.

For almost all n, a(n) = 0. [Charles R Greathouse IV, Jan 17 2012]

Links

Table of n, a(n) for n=1..65.

Example

a(2) = 17 because 2*17! = 711374856192000 contains every digit at least once.

Maple

a:={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}: for n from 1 to 100 do:ii:=0:for k from 1 to 50000 while(ii=0) do: x:=convert(convert(n*k!, base, 10), set):if x intersect a = a then ii:=1: printf(`%d, `, k):else fi:od:od:

Mathematica

Table[k=1; While[!Length[Union[IntegerDigits[n*k!]]] == 10, k++]; k, {n, 60}]

Crossrefs

Cf. A000142.

Sequence in context: A318090 A070716 A217894 * A160436 A105818 A085450

Adjacent sequences: A204595 A204596 A204597 * A204599 A204600 A204601

Keyword

nonn,base

Author

Michel Lagneau, Jan 17 2012

Status

approved