Determination of [nθ] by its Sequence of*Differences
- 1 December 1978
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 21 (4) , 441-446
- https://doi.org/10.4153/cmb-1978-077-0
Abstract
For any real numberθletwhere [x] denotes the greatest integer not exceedingx.A method is given for computingfθfrom its first few terms. A similar method is given for computing the characteristic functiongθ(n)of[nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequencesfθand gθdetermines the sequence[nθ] (n = 1, 2,…).Keywords
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