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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.

Keywords

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