given an infinite series of digits 0-9, where at least one of the digits is not equal to 0, what is the length of the smallest possible string of recursive digits that can be created by changing any amount of zeroes in the series.

ex. the series 1 0 0 0 0 2 3 0 0 0 1 0 0 0 0 0 0 . . .

a string you could make could be “1 0 0 0 0 2 3 0 0 0” by changing the following digits such that that string repeats ad infinitum.