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Found problems: 1

2015 Online Math Open Problems, 10
Tags: Online
For any positive integer $n$, define a function $f$ by \[f(n)=2n+1-2^{\lfloor\log_2n\rfloor+1}.\] Let $f^m$ denote the function $f$ applied $m$ times.. Determine the number of integers $n$ between $1$ and $65535$ inclusive such that $f^n(n)=f^{2015}(2015).$ [i]Proposed by Yannick Yao[/i]