John D. Cook • 6/27/2026

Height of harmonic numbers

This article continues a previous analysis of harmonic numbers written as reduced fractions, using base-2 bit lengths of numerators and denominators as a measure of height. It presents plots comparing actual and estimated heights, examines the error between them, and shows that relative error decreases noisily with n, consistent with asymptotic estimates linked to prime distribution.

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#Asymptotic Analysis #Harmonic Numbers #Reduced Fractions