On digit expansions with respect to linear recurrences

DOI10.1016/0022-314X(89)90011-5zbMath0676.10010OpenAlexW1976097360MaRDI QIDQ1122608

Attila Pethoe, Robert F. Tichy

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-314x(89)90011-5

zbMATH Keywords

asymptotic formulaFibonacci numbersdigit expansionslinear recurring sequencesecond-order linear recurrencesum-of-digit function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Recurrences (11B37) Radix representation; digital problems (11A63) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (23)

Associativity of recurrence multiplication ⋮ Representations of numbers and finite automata ⋮ Numbers with fixed sum of digits in linear recurrent number systems ⋮ Comments on the spectra of Pisot numbers ⋮ \(\beta\)-shift, numeration systems, and automata ⋮ Discrepancy Bounds for β $$\boldsymbol{\beta }$$ -adic Halton Sequences ⋮ \(S\)-parts of sums of terms of linear recurrence sequences ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Zeckendorf representation of multiplicative inverses modulo a Fibonacci number ⋮ Contributions to digit expansions with respect to linear recurrences ⋮ Redundancy of minimal weight expansions in Pisot bases ⋮ Digital sum problems and substitutions on a finite alphabet ⋮ Substitutions, coding prescriptions and integer representation ⋮ Unnamed Item ⋮ \(\alpha\)-expansions, linear recurrences, and the sum-of-digits function ⋮ Unique representations of integers using increasing sequences ⋮ Unique expansions of real numbers ⋮ The distribution of the sum-of-digits function ⋮ Summand minimality and asymptotic convergence of generalized Zeckendorf decompositions ⋮ The level of distribution of the sum-of-digits function of linear recurrence number systems ⋮ Finite beta-expansions ⋮ Generalized Zeckendorf expansions

Cites Work

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• A summation formula involving Fibonacci digits
• On the distribution of digits in Cantor representations of integers
• Sur la fonction sommatoire de la fonction 'somme des chiffres'
• On theβ-expansions of real numbers
• On algebraic equations with all but one root in the interior of the unit circle. To my teacher and former colleague Erhard Schmidt on his 75th birthday

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