Convergent series of integers with missing digits
Number Theory
2022-12-14 v3
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.
Cite
@article{arxiv.2010.06719,
title = {Convergent series of integers with missing digits},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:2010.06719},
year = {2022}
}
Comments
Minor changes, 8 pages