Geodesic
Partitioning of the interval $[0,1]$ induced
Sbornik. Mathematics, Tome 198 (2007) no. 5, pp. 661-690

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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. 
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     title = {Partitioning of the interval $[0,1]$ induced},
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     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_5_a3/}
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A. A. Dushistova. Partitioning of the interval $[0,1]$ induced. Sbornik. Mathematics, Tome 198 (2007) no. 5, pp. 661-690. http://geodesic.mathdoc.fr/item/SM_2007_198_5_a3/