Article
Algorithms and Bounds on the Sums of Powers of Consecutive Primes
Integers
(2024)
Abstract
We present and analyze an algorithm to enumerate all integers n≤x that can be written as the sum of consecutive kth powers of primes, for k>1. We show that the number of such integers n is asymptotically bounded by a constant times
ckx^(2/(k+1))/ (logx)^(2k/(k+1)),
where ck is a constant depending solely on k, roughly k2 in magnitude. This also bounds the asymptotic running time of our algorithm. We also present some computational results, using our algorithm, that imply this bound is, at worst, off by a constant factor near 0.6. Our work extends the previous work by Tongsomporn, Wananiyakul, and Steuding (2022) who examined consecutive sums of squares of primes.
Disciplines
Publication Date
Spring January 2, 2024
DOI
10.5281/zenodo.10450932
Citation Information
Cathal O'Sullivan, Jonathan P Sorenson and Aryn Stahl. "Algorithms and Bounds on the Sums of Powers of Consecutive Primes" Integers Vol. 24 (2024) p. A4 ISSN: 1553-1732 Available at: http://works.bepress.com/jonathan_sorenson/40/