On some conjectures concerning Stern's sequence and its twist
Number Theory
2010-10-19 v3
Abstract
In a recent paper, Roland Bacher conjectured three identities concerning Stern's sequence and its twist. In this paper we prove Bacher's conjectures. Possibly of independent interest, we also give a way to compute the Stern value (or twisted Stern value) of a number based solely on its binary expansion.
Cite
@article{arxiv.1008.0193,
title = {On some conjectures concerning Stern's sequence and its twist},
author = {Michael Coons},
journal= {arXiv preprint arXiv:1008.0193},
year = {2010}
}
Comments
12 pages. The new version has a corrected functional equation for $T(z)$. This changes the article significantly though the arguments remain similar