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

Diego Marques, and Alain Togbé. "On terms of linear recurrence sequences with only one distinct block of digits." Colloquium Mathematicae 124.2 (2011): 145-155. <http://eudml.org/doc/283813>.

@article{DiegoMarques2011,
abstract = {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.},
author = {Diego Marques, Alain Togbé},
journal = {Colloquium Mathematicae},
keywords = {Fibonacci numbers; Lucas numbers; digits; linear forms in logarithm; reduction method; linear recurrence sequence},
language = {eng},
number = {2},
pages = {145-155},
title = {On terms of linear recurrence sequences with only one distinct block of digits},
url = {http://eudml.org/doc/283813},
volume = {124},
year = {2011},
}

TY - JOUR
AU - Diego Marques
AU - Alain Togbé
TI - On terms of linear recurrence sequences with only one distinct block of digits
JO - Colloquium Mathematicae
PY - 2011
VL - 124
IS - 2
SP - 145
EP - 155
AB - 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.
LA - eng
KW - Fibonacci numbers; Lucas numbers; digits; linear forms in logarithm; reduction method; linear recurrence sequence
UR - http://eudml.org/doc/283813
ER -