Geodesic
On terms of linear recurrence sequences with only one distinct block of digits
Diego Marques1 ; Alain Togbé2
1 Departamento de Matemática Universidade de Brasília Brasília, DF, Brazil
2 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville, IN 46391, U.S.A.
Colloquium Mathematicum, Tome 124 (2011) no. 2, pp. 145-155.

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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.
DOI : 10.4064/cm124-2-1
Keywords: florian luca proved largest numbers only distinct digit fibonacci lucas sequences respectively paper terms linear recurrence sequence only block digits its expansion base geq application generalize lucas result finding fibonacci lucas numbers only distinct block digits length its decimal expansion

Diego Marques 1 ; Alain Togbé 2

1 Departamento de Matemática Universidade de Brasília Brasília, DF, Brazil
2 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville, IN 46391, U.S.A. 
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Diego Marques; Alain Togbé. On terms of linear recurrence sequences
 with only one distinct block of digits. Colloquium Mathematicum, Tome 124 (2011) no. 2, pp. 145-155. doi : 10.4064/cm124-2-1. http://geodesic.mathdoc.fr/articles/10.4064/cm124-2-1/

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