On some conjectures concerning Stern's sequence and its twist
Michael Coons
TL;DR
This paper proves three conjectures about Stern's sequence and its twist, providing a new binary expansion-based method to compute their values, which enhances understanding of their properties.
Contribution
It confirms Bacher's conjectures on Stern's sequence and introduces a binary expansion approach for computing Stern and twisted Stern values.
Findings
Proved three conjectures about Stern's sequence and its twist.
Developed a binary expansion method for computing Stern values.
Enhanced understanding of the properties of Stern's sequence.
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.
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