On simultaneous binary expansions of n and n²

2004/02/29 by Giuseppe Melfi
Mathematics · #math.NT #math.CO #msc:11A25

paper · pdf · doi:10.1016/j.jnt.2004.12.009

published as Journal of Number Theory, 111 (2005), 248 -- 256 · 10 pages

arxiv created 2004/03/02 · arxiv updated 2009/12/01

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 n². Some structure and asymptotic properties are proved and a conjecture about its counting function is discussed.

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