Inspired by Aakash Khandelwal

Geometry Level 5

If a0=sin2(π45)a_0=\sin^2\left (\dfrac{\pi}{45} \right) and an+1=4an(1an)a_{n+1}=4a_{n}(1-a_{n}) for n0n\geq 0, find the smallest positive integer nn such that an=a0a_n=a_0.

If you come to the conclusion that no such nn exists, enter 666.


Inspiration.

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