Benford’s Law under Zeckendorf Expansion

Sungkon Chang; Steven J. Miller

doi:10.1080/00150517.2024.2413585

Benford’s Law under Zeckendorf Expansion

Sungkon Chang
, Steven J. Miller

Mathematical Sciences

Williams College

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	304-335
Number of pages	32
Journal	Fibonacci Quarterly
Volume	63
Issue number	2
DOIs	https://doi.org/10.1080/00150517.2024.2413585
State	Published - Aug 14 2025

Scopus Subject Areas

Algebra and Number Theory

Keywords

Benford’s Law
Zeckendorf

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10.1080/00150517.2024.2413585

Cite this

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abstract = "In the literature, Benford{\textquoteright}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{\textquoteright}s Law should be under generalized Zeckendorf expansion.",

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AB - 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.

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KW - Zeckendorf

UR - https://www.scopus.com/pages/publications/105016259738

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Benford’s Law under Zeckendorf Expansion

Abstract

Scopus Subject Areas

Keywords

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