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(2): computer exploration by Jer)

Rule, a bit complicated?

I approached this using Excel and the MS Calculator that comes with Windows Op sys's.

Like Charlie I came to the conclusion that there is something in primes.

One set of figures that I recall [I destroyed my worksheet, or was it the Word doc, maybe both] looking at was: 11, 22, 33 ....  At that point I noted the multiples of primes.

Like Charlie I could not reconcile what I was seeing. 

Did Charlie mention the cycling of digits? I did notice this seemed to be occurring, was it with 7's?

Anyway, I trust Jer, that your solution is more readable, and easier to understand than the documentation that was given to me. 

Good problem, goes further than I suspected.

Posted by brianjn on 2006-09-25 23:36:50