Geodesic
Repdigits in generalized Pell sequences
Archivum mathematicum, Tome 56 (2020) no. 4, pp. 249-262 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For an integer $k\ge 2$, let $({n})_n$ be the $k-$generalized Pell sequence which starts with $0,\ldots ,0,1$ ($k$ terms) and each term afterwards is given by the linear recurrence ${n} = 2{n-1}+{n-2}+\cdots +{n-k}$. In this paper, we find all $k$-generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence $(P_n^{(2)})_n$.
For an integer $k\ge 2$, let $({n})_n$ be the $k-$generalized Pell sequence which starts with $0,\ldots ,0,1$ ($k$ terms) and each term afterwards is given by the linear recurrence ${n} = 2{n-1}+{n-2}+\cdots +{n-k}$. In this paper, we find all $k$-generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence $(P_n^{(2)})_n$.
DOI : 10.5817/AM2020-4-249
Classification : 11B39, 11J86
Keywords: generalized Pell numbers; repdigits; linear forms in logarithms; reduction method 
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Bravo, Jhon J.; Herrera, Jose L. Repdigits in generalized Pell sequences. Archivum mathematicum, Tome 56 (2020) no. 4, pp. 249-262. doi: 10.5817/AM2020-4-249

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