A204632 Least k such that n*k!! contains every digit at least once.

34, 30, 37, 28, 27, 28, 27, 39, 34, 34, 36, 36, 35, 27, 30, 34, 25, 34, 31, 30, 27, 29, 27, 30, 33, 35, 34, 44, 31, 37, 25, 32, 33, 28, 33, 36, 26, 30, 35, 28, 29, 32, 31, 30, 28, 27, 29, 38, 30, 27, 25, 35, 33, 29, 36, 33, 37, 32, 34, 28, 29, 33, 26, 22, 29

Offset

1,1

Comments

A property of this sequence: the arithmetic mean s(x) = (1/x) *Sum_{k = 1..x} a(k) is very slowly decreasing when x increases. For example, s(100) = 30.89; s(1000) = 29.795 ; s(10000) = 28.1319 ; s(100000) = 26.53411. For almost all n, a(n) = 0 (see A204598).

Links

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

Example

a(2) = 30 because 2*30!! =  2* 42849873690624000 = 85699747381248000 contains every digit at least once.

Mathematica

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

Crossrefs

Cf. A006882, A204598.

Sequence in context: A214038 A070727 A298894 * A098023 A302209 A022990

Adjacent sequences: A204629 A204630 A204631 * A204633 A204634 A204635

Keyword

nonn,base

Author

Michel Lagneau, Jan 17 2012

Status

approved