×

zbMATH — the first resource for mathematics

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 \(1\)
PDF BibTeX XML Cite
Full Text: DOI