Determination of [nθ] by its Sequence of*Differences

Fraenkel, A. S. ; Mushkin, M. ; Tassa, U.

Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 441-446

Résumé

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,...).

Détail

DOI : 10.4153/CMB-1978-077-0

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