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Determination of [nθ] by its Sequence of*Differences

Published online by Cambridge University Press:  20 November 2018

A. S. Fraenkel ,
M. Mushkin  and
U. Tassa
A. S. Fraenkel
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
M. Mushkin
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
U. Tassa
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
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Abstract

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For any real number θ let where [x] denotes the greatest integer not exceeding x. A method is given for computing fθ from its first few terms. A similar method is given for computing the characteristic function gθ(n) of [nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequences fθ and gθ determines the sequence [nθ] (n = 1, 2,…).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 441 - 446
Copyright
Copyright © Canadian Mathematical Society 1978

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