English

New normality constructions for continued fraction expansions

Number Theory 2015-07-03 v1 Dynamical Systems

Abstract

Adler, Keane, and Smorodinsky showed that if one concatenates the finite continued fraction expansions of the sequence of rationals 12,13,23,14,24,34,15, \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5}, \cdots into an infinite continued fraction expansion, then this new number is normal with respect to the continued fraction expansion. We show a variety of new constructions of continued fraction normal numbers, including one generated by the subsequence of rationals with prime numerators and denominators: 23,25,35,27,37,57,. \frac{2}{3}, \frac{2}{5}, \frac{3}{5}, \frac{2}{7}, \frac{3}{7}, \frac{5}{7},\cdots.

Keywords

Cite

@article{arxiv.1507.00390,
  title  = {New normality constructions for continued fraction expansions},
  author = {Joseph Vandehey},
  journal= {arXiv preprint arXiv:1507.00390},
  year   = {2015}
}
R2 v1 2026-06-22T10:04:07.333Z