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 re(5): General solution by Old Original Oskar!)

Yes, I typed 2 instead of 10.  I must have had binary on the brain, such as it is! I'm old, you know.

Posted by Richard on 2006-09-27 15:52:05