2009 OIM Problems/Problem 5

Problem

The sequence $a_n$ is defined by $a_1 = 1, a_{2k} = 1 + a_k$ , and $a_{2k+1} = \frac{1}{a_{2k}}, for all integer$ k \ge 1$. Prove that every positive rational number appears exactly once in this sequence.

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

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2009 OIM Problems/Problem 5

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