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

Giuseppe Melfi

doi:10.1016/j.jnt.2004.12.009

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

Number Theory 2007-05-23 v2 Combinatorics

Authors: 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.

Keywords

integer sequences and recurrences collatz conjecture exponential sums

Cite

@article{arxiv.math/0402458,
  title  = {On simultaneous binary expansions of $n$ and $n^2$},
  author = {Giuseppe Melfi},
  journal= {arXiv preprint arXiv:math/0402458},
  year   = {2007}
}

Comments

10 pages

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