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June 2012 How slowly can a bounded sequence cluster?
John Bentin
Funct. Approx. Comment. Math. 46(2): 195-204 (June 2012). DOI: 10.7169/facm/2012.46.2.5


We propose a simple measure of how slowly a bounded real sequence clusters. This measure, called \emph{separation}, is the infimum, over all finite segments of the sequence with at least two terms, of the ratio of the least distance between the terms in the segment to the general supremum of such a distance for a segment of that length. An example of a highly separated sequence is given. To create a more separated sequence, we modify van der Corput's construction, replacing the powers of a base by the even-numbered terms of the Fibonacci sequence. The result coincides initially with the sequence built stepwise by maximizing separation for each extra term. We conjecture that these sequences are the same and of maximal separation.


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John Bentin. "How slowly can a bounded sequence cluster?." Funct. Approx. Comment. Math. 46 (2) 195 - 204, June 2012.


Published: June 2012
First available in Project Euclid: 25 June 2012

zbMATH: 1292.11021
MathSciNet: MR2931666
Digital Object Identifier: 10.7169/facm/2012.46.2.5

Primary: 11B05
Secondary: 11B39, 11B83

Rights: Copyright © 2012 Adam Mickiewicz University


Vol.46 • No. 2 • June 2012
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