Geodesic
A curious bijection on natural numbers
Journal of integer sequences, Tome 12 (2009) no. 8
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.
Classification : 11B13
Keywords: shapovalov, curious bijection, greedy algorithm 
@article{JIS_2009__12_8_a0,
     author = {Venkatachala,  B.J.},
     title = {A curious bijection on natural numbers},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {8},
     zbl = {1201.11018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a0/}
}
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Venkatachala,  B.J. A curious bijection on natural numbers. Journal of integer sequences, Tome 12 (2009) no. 8. http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a0/