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Generalized Lucas Numbers Which are Concatenations of Two Repdigits

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Abstract

A generalization of the well–known Lucas sequence is the k–Lucas sequence with some fixed integer \(k\ge 2\). The first k terms of this sequence are \(0,\ldots ,0,2,1\), and each term afterwards is the sum of the preceding k terms. In this paper, we find all k–Lucas numbers that are concatenations of two repdigits. This generalizes a prior result which dealt with the above problem for the particular case of Lucas numbers.

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Acknowledgements

We thank the reviewers for their detailed comments and suggestions which significantly contributed to improving the quality of the manuscript. J. J. B. was supported in part by Project VRI ID 5385 (Universidad del Cauca). C. A. G. was supported in part by Project 71280 (Universidad del Valle).

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del Cauca, Calle 5 No. 4–70, Popayán, Colombia

    Eric F. Bravo & Jhon J. Bravo

  2. Departamento de Matemáticas, Universidad del Valle, Calle 13 No. 100–00, Cali, Colombia

    Carlos A. Gómez

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  1. Eric F. Bravo
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  2. Jhon J. Bravo
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  3. Carlos A. Gómez
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Correspondence to Eric F. Bravo.

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The authors are members of the research group: Matemática Discreta y Aplicaciones: ERM (MATDIS).

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Bravo, E.F., Bravo, J.J. & Gómez, C.A. Generalized Lucas Numbers Which are Concatenations of Two Repdigits. Results Math 76, 139 (2021). https://doi.org/10.1007/s00025-021-01456-9

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