The fractional part of \(n\theta + \phi\) and Beatty sequences

DOI10.5802/jtnb.148zbMath0849.11027OpenAlexW2322112535MaRDI QIDQ1910677

Takao Komatsu

Publication date: 12 November 1996

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1995__7_2_387_0

zbMATH Keywords

continued fractioncharacteristic wordone-sided approximationsBeatty sequencesorting problem

Mathematics Subject Classification ID

Continued fractions (11A55) Special sequences and polynomials (11B83) Automata sequences (11B85)

Related Items (7)

Prime divisors in Beatty sequences ⋮ Covering numbers: Arithmetics and dynamics for rotations and interval exchanges ⋮ Primes in Beatty sequence ⋮ Substitution invariant Sturmian bisequences ⋮ Non-residues and primitive roots in Beatty sequences ⋮ Oscillations of coefficients of primitive cusp forms over some special sequences ⋮ Combinatorial, ergodic and arithmetic properties of the Tribonacci substitution

Cites Work

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• Arithmetical properties of a certain power series
• On the generating function of the integer part: \([n\alpha{}+ \gamma{}\)]
• Some classes of transcendental numbers
• Beatty Sequences, Continued Fractions, and Certain Shift Operators
• Determination of [nθ by its Sequence of^*Differences]
• Descriptions of the Characteristic Sequence of an Irrational
• On the characteristic word of the inhomogeneous Beatty sequence
• A certain power series associatedwith a Beatty sequence

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