On terms of linear recurrence sequences with only one distinct block of digits

• Autorzy: Diego Marques , Alain Togbé
• Języki publikacji: EN

Abstrakty

EN

In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.

Kategorie tematyczne

• 11A63: Radix representation; digital problems
• 11B37: Recurrences
• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11J86: Linear forms in logarithms; Baker's method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 124
• Numer: 2
• Strony: 145-155

Daty

wydano

2011

Twórcy

autor

Diego Marques

• Departamento de Matemática, Universidade de Brasília, Brasília, DF, Brazil

autor

Alain Togbé

• Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville, IN 46391, U.S.A.

Identyfikatory

DOI

10.4064/cm124-2-1