A generating function technique for Beatty sequences and other step sequences

DOI10.1006/jnth.2001.2743zbMath1044.11009OpenAlexW2108109197MaRDI QIDQ700198

Kevin O'Bryant

Publication date: 30 September 2002

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2001.2743

zbMATH Keywords

generating functionLambert seriesBeatty sequenceFraenkel conjecturecomplementary sequenceFarey fraction

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) (zeta (s)) and (L(s, chi)) (11M06) Other combinatorial number theory (11B75) Special sequences and polynomials (11B83) Hurwitz and Lerch zeta functions (11M35) Representation functions (11B34)

Related Items (8)

Prime divisors in Beatty sequences ⋮ Almost Beatty Partitions ⋮ On \(m\)-covering families of Beatty sequences with irrational moduli ⋮ On the meromorphic continuation of Beatty zeta-functions and Sturmian Dirichlet series ⋮ Primes in Beatty sequence ⋮ On certain zeta functions associated with Beatty sequences ⋮ Non-residues and primitive roots in Beatty sequences ⋮ Oscillations of coefficients of primitive cusp forms over some special sequences

Cites Work

• Certain sequences of Wythoffian matrices, and maximal geometric progressions therein
• On the generating function of the integer part: \([n\alpha{}+ \gamma{}\)]
• Irrational Power Series
• A Naturally Occurring Function Continuous Only at Irrationals
• Half-Silvered Mirrors and Wythoff's Game
• Determination of [nθ by its Sequence of^*Differences]
• Iterated Floor Function, Algebraic Numbers, Discrete Chaos, Beatty Subsequences, Semigroups
• Descriptions of the Characteristic Sequence of an Irrational
• Irrational power series II
• The Bracket Function and Complementary Sets of Integers
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