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Sequential partitioning. (English) Zbl 0771.11031
Starting from a practical problem, the author considers sequences $$\{x_ n\}$$ with $$x_ 1=1$$, $$x_ n=x_{2n}+x_{2n+1}$$, and $$x_ 1\geq x_ 2\geq x_ 3\dots>0$$ which he calls leapfrog sequences. He asks for leapfrog sequences $$\{x_ n\}$$ for which $$\limsup(nx_ n)$$ the minimal or for which $$\liminf(nx_ n)$$ is maximal. In both cases the logarithmic sequence $$x_ n=\log_ 2((n+1)/n)$$ is optimal.
##### MSC:
 11K06 General theory of distribution modulo $$1$$
##### Keywords:
uniform distribution; leapfrog sequences
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