Weighted Mediants and Fractals
Abstract
In this paper we study a natural generalization of the SternBrocot sequences which comes from the introduction of weighted mediants. We focus our attention on the case $k = 3$, in which $(2a + c)/(2b + d)$ and $(a + 2c)/(b + 2d)$ are the two mediants inserted between $a/b$ and $c/d$. We state and prove several properties about the crossdifferences of SternBrocot sequences with $k = 3$, and give a proof of the fractallike rule that describes the crossdifferences of the unit $k = 3$ SternBrocot sequences, i.e. the one with usual starting terms $0/1, 1/1$ and with reduction of fractions.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.01475
 Bibcode:
 2017arXiv171101475A
 Keywords:

 Mathematics  Number Theory;
 11B99;
 28A80
 EPrint:
 22 pages, 11 figures