[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b191047

ON THE DENOMINATORS OF 𝜀-HARMONIC NUMBERS

Wu, Bing-Ling (School of Science Nanjing University of Posts and Telecommunications)
Yan, Xiao-Hui (School of Mathematical Sciences and Institute of Mathematics Nanjing Normal University)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.6, 2020 , pp. 1383-1392 More about this Journal

Abstract

Let H_n be the n-th harmonic number and let ν_n be its denominator. Shiu proved that there are infinitely many positive integers n with ν_n = ν_n+1. Recently, Wu and Chen proved that the set of positive integers n with ν_n = ν_n+1 has density one. They also proved that the same result is true for the denominators of alternating harmonic numbers. In this paper, we prove that the result is true for the denominators of 𝜀-harmonic numbers, where 𝜀 = {𝜀_i}^∞_i=1 is a pure recurring sequence with 𝜀_i ∈ {-1, 1}.

Keywords

Harmonic numbers; p-adic valuation; asymptotic density; recurring sequences;

Citations & Related Records

Reference

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