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The shortest harmonic sums with decreasing denominator

Wouter van Doorn

math.NTarXiv:2609.00104

Abstract

For a positive integer a, let b(a) be the smallest integer b > a such that the denominator of 1a + 1a+1 + ·s + 1b is smaller than the denominator of 1a + 1a+1 + ·s + 1b-1. Recently it was shown that the limit inferior a ∞ (b(a) - a a) exists and is positive. Here we find its exact value.

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