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On partitions of the unit interval generated by Brocot sequences

Anna Dushistova
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Abstract

Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $σ_β(F_n)=\sum_{i=1}^{N(n)} p_{i, n}^β $,which improves known estimates.

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Anna Dushistova. 2007-12-15. On partitions of the unit interval generated by Brocot sequences. https://arxiv.org/abs/math/0512598

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