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April 24th, 2012, 04:27 PM   #1
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An interesting fraction




The decimal representation contains all the 3-digit numbers except 998
[color=beige]. . [/color]and the 2997-digit cycle repeats forever.

This is just one of a family of such fractions.
Can you determine the underlying characteristic?

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April 24th, 2012, 06:17 PM   #2
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Re: An interesting fraction

I looked at the factorization of the denominator, and found:



So, next I looked at:



Thus, I conjecture that the family you speak of is:

where

where the decimal representation contains all of the n digit numbers except and the period is .
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