This article is cited in 2 papers

Partitioning of the interval $[0,1]$ induced by the Brocot sequences

A. A. Dushistova

M. V. Lomonosov Moscow State University

Abstract: Let $p_{i,n}$, $i=1,\dots,2^{n-1}$, be the lengths of the intervals between successive points in the Brocot sequence $F_n$. An asymptotic formula for the quantity $\sigma(F_n)=\sum_{i=1}^{N(n)}p_{i,n}^\beta$, which improves the previously known estimates, is obtained.
Bibliography: 5 titles.

UDC: 511.216

MSC: Primary 11B99; Secondary 11J70, 37A45

Received: 10.11.2005 and 17.11.2006

DOI: 10.4213/sm1436

 English version: Sbornik: Mathematics, 2007, 198:5, 661–690

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