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On the distance between generalized Fibonacci numbers

Volume 140 / 2015

Jhon J. Bravo, Carlos A. Gómez, Florian Luca Colloquium Mathematicum 140 (2015), 107-118 MSC: Primary 11B39; Secondary 11J86. DOI: 10.4064/cm140-1-9


For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n}$ be the $k$-Fibonacci sequence which starts with $0,\ldots ,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. This paper completes a previous work of Marques (2014) which investigated the spacing between terms of distinct $k$-Fibonacci sequences.


  • Jhon J. BravoDepartamento de Matemáticas
    Universidad del Cauca
    Calle 5 No. 4–70
    Popayán, Colombia
  • Carlos A. GómezDepartamento de Matemáticas
    Universidad del Valle
    Calle 13 No. 100–00
    Cali, Colombia
  • Florian LucaSchool of Mathematics
    University of the Witwatersrand
    P.O. Box Wits 2050
    Johannesburg, South Africa

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