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): General solution by Federico Kereki)

The answer for D digits should read: X, if X divides 10^D-1, and doesn't divide any 10^E-1 for 0<E<D.

Posted by Old Original Oskar! on 2006-09-26 16:14:41