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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-1,
author = {Diego Marques and Alain Togb\'e},
title = {On terms of linear recurrence sequences with only one distinct block of digits},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {145-155},
zbl = {1246.11036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-1}
}
Diego Marques; Alain Togbé. On terms of linear recurrence sequences with only one distinct block of digits. Colloquium Mathematicae, Tome 122 (2011) pp. 145-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-1/