A081664 For the smallest q for which there exists a fraction p/q containing n in its decimal expansion, this sequence gives the smallest p.

1, 1, 1, 2, 1, 2, 3, 4, 9, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 6, 1, 4, 3, 1, 1, 3, 5, 8, 1, 1, 5, 4, 3, 2, 1, 2, 5, 1, 7, 4, 5, 2, 1, 12, 1, 1, 5, 1, 2, 5, 5, 9, 1, 7, 13, 3, 2, 5, 4, 9, 13, 2, 19, 11, 1, 7, 1, 3, 11, 2, 3, 1, 7, 11, 19, 4, 2, 1, 5, 2, 1, 13, 7, 8, 1, 9, 11, 1, 14, 1, 19, 24, 33, 49

Offset

1,4

Comments

Inspired by problem 14 on the 2003 American Invitational Mathematics Examination, which asked for a(251). There are some slightly different versions of this sequence. For example, you could consider 1/2 = .5 or 1/2 = .50000...; I chose the latter interpretation here.

Links

Table of n, a(n) for n=1..98.

American Mathematics Competitions, Problem 14

Example

a(6) = 2 because 2/3 = .6...; a(24) = 6 because 6/25 = .24

Crossrefs

A081665 gives the denominators.

Sequence in context: A325841 A076480 A002730 * A224926 A117673 A107946

Adjacent sequences: A081661 A081662 A081663 * A081665 A081666 A081667

Keyword

base,frac,nonn

Author

Joshua Zucker, Mar 26 2003

Status

approved