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

Giuseppe Melfi

doi:10.1016/j.jnt.2004.12.009

paper

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

arXiv:math/0402458 · doi:10.1016/j.jnt.2004.12.009

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.

10 pages

On simultaneous binary expansions of n and n2

Abstract

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