Benford's Law under Zeckendorf expansion

TL;DR

This paper explores how Benford's Law applies to Zeckendorf expansions, extending the concept beyond traditional base-b representations to understand digit distribution in Fibonacci-based number systems.

Contribution

It introduces a generalized Benford's Law for Zeckendorf expansions, providing a new perspective on digit distribution in non-standard number representations.

Findings

Benford's Law can be extended to Zeckendorf expansions

The distribution of leading digits differs from classical Benford's Law in this context

The paper proposes a generalized law applicable to Fibonacci-based expansions

Abstract

In the literature, Benford's Law is considered for base-b expansions where b>1 is an integer. In this paper, we investigate the distribution of leading "digits" of a sequence of positive integers under other expansions such as Zeckendorf expansion, and declare what Benford's Law should be under generalized Zeckendorf expansion.