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Curious Generalized Fibonacci Numbers

Author

Listed:
  • Jose L. Herrera

    (Departamento de Matemáticas, Universidad del Cauca, Popayán 190003, Colombia)

  • Jhon J. Bravo

    (Departamento de Matemáticas, Universidad del Cauca, Popayán 190003, Colombia)

  • Carlos A. Gómez

    (Departamento de Matemáticas, Universidad del Valle, Cali 25360, Colombia)

Abstract

A generalization of the well-known Fibonacci sequence is the k − Fibonacci sequence whose first k terms are 0 , … , 0 , 1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k -Fibonacci numbers that are curious numbers (i.e., numbers whose base ten representation have the form a ⋯ a b ⋯ b a ⋯ a ) . This work continues and extends the prior result of Trojovský, who found all Fibonacci numbers with a prescribed block of digits, and the result of Alahmadi et al., who searched for k -Fibonacci numbers, which are concatenation of two repdigits.

Suggested Citation

  • Jose L. Herrera & Jhon J. Bravo & Carlos A. Gómez, 2021. "Curious Generalized Fibonacci Numbers," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2588-:d:656839
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    References listed on IDEAS

    as
    1. Pavel Trojovský, 2020. "Fibonacci Numbers with a Prescribed Block of Digits," Mathematics, MDPI, vol. 8(4), pages 1-7, April.
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    Cited by:

    1. Alaa Altassan & Murat Alan, 2023. "Almost Repdigit k -Fibonacci Numbers with an Application of k -Generalized Fibonacci Sequences," Mathematics, MDPI, vol. 11(2), pages 1-16, January.

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