Shifting Zeckendorf and Chung-Graham representations

TL;DR

This paper revisits properties of integers with Zeckendorf and Chung-Graham representations, employing shift operator techniques and Walnut software to re-prove known results.

Contribution

It introduces a new proof approach using shift operators and computational tools for properties of these number representations.

Findings

Re-proved key properties of Zeckendorf and Chung-Graham representations

Demonstrated the effectiveness of Walnut software in number representation proofs

Provided insights into the structure of these representations

Abstract

We re-prove some results about integers whose Zeckendorf and Chung-Graham representations satisfy certain conditions. We use properties of the shift operator and use the software package {\tt Walnut}.