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If a0=sin2(π45)a_0=\sin^2\left (\dfrac{\pi}{45} \right)a0=sin2(45π) and an+1=4an(1−an)a_{n+1}=4a_{n}(1-a_{n})an+1=4an(1−an) for n≥0n\geq 0n≥0, find the smallest positive integer nnn such that an=a0a_n=a_0an=a0.
If you come to the conclusion that no such nnn exists, enter 666.
Inspiration.
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