# An eventually periodic sequence

Number Theory Level pending

Let us call a real sequence $$\{a_n\}_{n\ge 0}$$ eventually periodic if $$\exists$$ positive numbers $$m,N$$ such that $$a_{n+N}=a_n,\ \forall n\ge m$$. The smallest such $$N$$ is called the period of the eventually periodic sequence.

Is the following sequence eventually periodic? $c_0=\frac{1}{2017},\quad c_{n}=|1-|1-2c_{n-1}||,\quad n\ge 1$

If it is, find its period.

Put $$666$$ as your answer if you think that the sequence is not eventually periodic.

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