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

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

2004-02-27

arxiv.org/abs/math/0402458v2

Journal of Number Theory, 111 (2005), 248 -- 256

Mathematics

Number Theory

10 pages

Scientific paper

10.1016/j.jnt.2004.12.009

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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