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Repdigits in generalized Pell sequences

Jhon J. Bravo; Jose L. Herrera

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 4, page 249-262
  • ISSN: 0044-8753

Abstract

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For an integer k ≥ 2 , let ( n ) n be the k - generalized Pell sequence which starts with 0 , ... , 0 , 1 ( k terms) and each term afterwards is given by the linear recurrence n = 2 n - 1 + n - 2 + ⋯ + 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 .

How to cite

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Bravo, Jhon J., and Herrera, Jose L.. "Repdigits in generalized Pell sequences." Archivum Mathematicum 056.4 (2020): 249-262. <http://eudml.org/doc/296926>.

@article{Bravo2020,
abstract = {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 $(P_n^\{(2)\})_n$.},
author = {Bravo, Jhon J., Herrera, Jose L.},
journal = {Archivum Mathematicum},
keywords = {generalized Pell numbers; repdigits; linear forms in logarithms; reduction method},
language = {eng},
number = {4},
pages = {249-262},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Repdigits in generalized Pell sequences},
url = {http://eudml.org/doc/296926},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Bravo, Jhon J.
AU - Herrera, Jose L.
TI - Repdigits in generalized Pell sequences
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 4
SP - 249
EP - 262
AB - 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 $(P_n^{(2)})_n$.
LA - eng
KW - generalized Pell numbers; repdigits; linear forms in logarithms; reduction method
UR - http://eudml.org/doc/296926
ER -

References

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