A081665 Smallest integer q for which there exists a fraction p/q containing n in its decimal expansion.

1, 4, 3, 5, 2, 3, 4, 5, 10, 1, 9, 8, 15, 7, 13, 6, 17, 11, 21, 5, 14, 9, 13, 25, 4, 15, 11, 7, 17, 10, 16, 25, 3, 23, 14, 11, 8, 13, 23, 5, 12, 7, 16, 9, 11, 13, 17, 25, 51, 2, 27, 17, 13, 11, 9, 16, 7, 12, 22, 5, 13, 8, 11, 14, 20, 3, 28, 16, 13, 10, 7, 11, 15, 27, 4, 13, 9, 14, 24, 5, 11

Offset

1,2

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..81.

American Mathematics Competitions, Problem 14

Example

a(6) = 3 because 2/3 = .6...; a(42) = 7 because 1/7 = .142...

Crossrefs

A081664 gives the numerators.

Sequence in context: A011397 A352692 A339579 * A131911 A254037 A321154

Adjacent sequences: A081662 A081663 A081664 * A081666 A081667 A081668

Keyword

base,frac,nonn

Author

Joshua Zucker, Mar 26 2003

Status

approved