Comparing the growth of the prime numbers to the natural numbers

Authors

• Michael Brilleslyper, United States Air Force Academy
• Nathan Wakefield, University of Nebraska - Lincoln
• Austin J. Wallerstein, Air Force Institute of Technology
• Bradley Warner, United States Air Force Academy

Document Type

Article

Publication Date

2016

Department

Department of Engineering Physics

School or Division

Graduate School of Engineering and Management

Digital Object Identifier

10.1080/00150517.2016.12427841

Source Publication

The Fibonacci Quarterly (ISSN 0015-0517 | eISSN 2641-340X)

Abstract

We define a new method of measuring the rate of divergence for an increasing positive sequence of integers. We introduce the growth function for such a sequence and its associated growth limit. We use these tools to study the divergence rate for the natural numbers, polynomial and exponential-type sequences, and the prime numbers. We conclude with a number of open questions concerning general properties and characterizations of growth functions and the set of possible growth limits.

Comments

Co-author A. Wallerstein was an AFIT PhD student at the time of this article. AFIT-ENP-DS-18-D-009, December 2018)

Reviewed at MR3473263

The article was published in print as cited below, by the Fibonacci Association in 2016.  Taylor and Francis issued the digital version of the article in September 2024.

Recommended Citation

Brilleslyper, M. A., Wakefield, N., Wallerstein, A. J., & Warner, B. (2016). Comparing the growth of the prime numbers to the natural numbers. Fibonacci Quarterly, 54(1), 65–71.