On terms of linear recurrence sequences with only one distinct block of digits
Volume 124 / 2011
Colloquium Mathematicum 124 (2011), 145-155
MSC: 11A63, 11B37, 11B39, 11J86.
DOI: 10.4064/cm124-2-1
Abstract
In 2000, Florian Luca proved that $F_{10}=55$ and $L_5=11$ 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 $g\geq 2$. 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.
