Convergent series of integers with missing digits

TL;DR

This paper extends Kempner's classical theorem by exploring larger sets of positive integers with missing digits, demonstrating that their harmonic series also converges, thus broadening the understanding of digit-restricted integer sets.

Contribution

The paper generalizes Kempner's theorem to larger families of missing digit sets, showing their harmonic series converge, which was not previously established.

Findings

Harmonic series of missing digit integers converges

Extended convergence results to broader digit-restriction sets

Provides new insights into digit-based integer sets

Abstract

A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with convergent harmonic series.