Modified Stern-Brocot Sequences

2013/01/29 by Aiylam, Dhroova
#11Z02 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1301.6807

Abstract

We present the classical Stern-Brocot tree and provide a new proof of the fact that every rational number between 0 and 1 appears in the tree. We then generalize theStern-Brocot tree to allow for arbitrary choice of starting terms, and prove that in all cases the tree maintains the property that every rational number between the two starting terms appears exactly once.

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