2016 is absolutely awesome 3

Logic Level 2

For any positive integer \(k\) let \(f_1(k)\) denote the sum of the squares of the digits of \(k\) (when written in decimal), and for \(n \ge 2\) define \(f_n(k)\) iteratively by \(f_n(k)=f_1(f_{n−1}(k))\).

Find \(f_{2017}(2016)\).

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