On the denominators of $\varepsilon$-harmonic numbers
Bull. Korean Math. Soc. 2020 Vol. 57, No. 6, 1383-1392 https://doi.org/10.4134/BKMS.b191047 Published online September 1, 2020 Printed November 30, 2020
Bing-Ling Wu, Xiao-Hui Yan Nanjing University of Posts and Telecommunications; Anhui Normal University
Abstract : Let $H_n$ be the $n$-th harmonic number and let $v_n$ be its denominator. Shiu proved that there are infinitely many positive integers $n$ with $v_n =v_{n+1}$. Recently, Wu and Chen proved that the set of positive integers $n$ with $v_n = v_{n+1}$ 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 $\varepsilon$-harmonic numbers, where $\varepsilon=\{ \varepsilon_i \}_{i=1}^\infty $ is a pure recurring sequence with $\varepsilon_i\in \{-1,1\}$.
