The decimal expansion of 1/271 repeats with a period of length 5:
.003690036900369 ...

However, it is not the smallest number q for which the decimal expansion of 1/q has a repetition length of 5.

Find the smallest q so that the decimal expansion of 1/q has repetition length n for each of {1, 2, ..., 10}

Is there a simple way of finding such a number?

(In reply to General solution by Federico Kereki)

Your numbers are not all minimums.  See Charlie's posts.

It appears you assumed q is a prime number.  Your method still makes sense, but needs adjusting.

Posted by Jer on 2006-09-26 11:17:03