2007 OIM Problems/Problem 1

Problem

Given a positive integer $m$, the sequence {$a_n$} is defined as follows:

\[a_1=\frac{m}{2},\;a_{n+1}=a_n\left\lceil a_n \right\rceil,\; \text{ if }n\ge 1\]

Find all values of $m$ for which $a_{2007}$ is the first integer that appears in the succession.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions