Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.11.28
  • Accepted : 2020.06.15
  • Published : 2020.11.30
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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}.

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References

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