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

Volume 124 / 2011

Diego Marques, Alain Togbé Colloquium Mathematicum 124 (2011), 145-155 MSC: 11A63, 11B37, 11B39, 11J86. DOI: 10.4064/cm124-2-1


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.


  • Diego MarquesDepartamento de Matemática
    Universidade de Brasília
    Brasília, DF, Brazil
  • Alain TogbéMathematics Department
    Purdue University North Central
    1401 S, U.S. 421
    Westville, IN 46391, U.S.A.

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