Abstract
Let Hn be the n-th harmonic number and let νn be its denominator. Shiu proved that there are infinitely many positive integers n with νn = νn+1. Recently, Wu and Chen proved that the set of positive integers n with νn = νn+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 = {𝜀i}∞i=1 is a pure recurring sequence with 𝜀i ∈ {-1, 1}.