# How to find the length of an indefinitely repeated sequence in a list

Here, I am not looking for simply a repeated element, but an indefinitely repeated sequence. For example, if I have the list

{1,3,4,3,4,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3}


I would like Mathematica to output $$3$$, since the sequence $$(2,3,3)$$ (with length 3) repeats until the end of the sequence after a certain point. Note, the repeated sequence needs to continue until the end of the list. For example, the sequence $$(3,4)$$ does repeat itself near the beginning of the list, however I would not want an output of $$2$$ due to this repetition since the sequence $$(3,4)$$ does not continue after a certain point.

More formally: If I input a list for which the $$i^{th}$$ element is $$x_i$$, I want Mathematica to output the smallest number $$n$$ for which $$x_i=x_{i+n}$$ for all sufficiently large $$i$$.

What function/code would allow me to input a list and then would output the desired result?

Length@Last@FindTransientRepeat[

For whether the second argument 2 is sufficient for all your inputs, see FindTransientRepeat.