Preprint; last accessed January 14, 2025.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: In this paper, we explore whether certain recurrence relations satisfy Benford’s law. We prove that the Fibonacci sequence follows Benford’s law, generalizing our findings to other families of linear recurrences. We investigate if the terms and convergents of certain simple continued fractions follow Benford’s Law. We find an explicit formula for the recurrence relation of the numerators and denominators of the convergents of quadratic irrationals to show these sequences follow Benford’s Law. Furthermore, we make use of the GaussKuzmin distribution and the Levy’s constant to make statements about all simple continued fractions, except for a set of measure zero, concerning Benford’s Law. Lastly, we investigate the simple continued fractions of certain transcendentals to make conjectures related to Benford’s Law.
Bibtex:
@misc{,
title={Benford’s Law in Linear Recurrences and Continued Fractions},
author={Michelle Z. He and Brian Huang and Aadeesh Shastry and Mirilla Zhu},
year={2017},
url={https://api.semanticscholar.org/CorpusID:133593898}
}
Reference Type: Preprint
Subject Area(s): Analysis, Number Theory