Properties of the cumulated deficient binary digit sum
Number Theory
2019-11-12 v3
Abstract
The sequence A268289 from the On-Line Encyclopedia of Integer Sequences, namely the cumulated differences between the number of digits 1 and the number of digits 0 in the binary expansion of consecutive integers, is studied here. This sequence happens to match a sequence of cardinalities of some specific sets. Furthermore, it can also be expressed by using the Takagi function. The three different definitions have their own properties and combining them together lead to some new identities.
Keywords
Cite
@article{arxiv.1908.02250,
title = {Properties of the cumulated deficient binary digit sum},
author = {Thomas Baruchel},
journal= {arXiv preprint arXiv:1908.02250},
year = {2019}
}