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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, 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
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
KEYWORD
base,frac,nonn
AUTHOR
Joshua Zucker, Mar 26 2003
STATUS
approved