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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70302A 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 pagesNumber TheoryCombinatorics11A25On simultaneous binary expansions of $n$ and $n^2$text