On some conjectures concerning Stern's sequence and its twist

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.

12 pages. The new version has a corrected functional equation for $T(z)$. This changes the article significantly though the arguments remain similar