On partitions of the unit interval generated by Brocot sequences
Anna Dushistova
Abstract
Let pi, n, i=1,..., N(n)=2n-1 be the lengths of intervals between the neighboring fractions of Brocot sequence Fn . We obtain an asymptotic formula for σβ(Fn)=Σi=1N(n) pi, nβ ,which improves known estimates.
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