Summary: We give a greedy algorithm for describing an enumeration of the set of all natural numbers such that the sum of the first $n$ terms of the sequence is divisible by $n$ for each natural number $n$. We show that this leads to a bijection $f$ of the set of all natural numbers onto itself that has some nice properties. We also show that the average function of the first $n$ terms of the sequence satisfies a functional equation which completely describes all the properties of the function $f$. In particular, $f$ turns out to be an $involution$ on the set of all natural numbers.

11B13

shapovalov, curious bijection, greedy algorithm