On simultaneous binary expansions of $n$ and $n^2$

Giuseppe Melfi

doi:10.1016/j.jnt.2004.12.009

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On simultaneous binary expansions of $n$ and $n^2$

Giuseppe Melfi

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Abstract

A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers $n$ for which the sum of binary digits is equal to the sum of binary digits of $n^2$. Some structure and asymptotic properties are proved and a conjecture about its counting function is discussed.

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Giuseppe Melfi. 2004-03-02. On simultaneous binary expansions of $n$ and $n^2$. https://doi.org/10.1016/j.jnt.2004.12.009

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