Geodesic
On the distance between generalized Fibonacci numbers
Jhon J. Bravo1 ; Carlos A. Gómez2 ; Florian Luca3
1Departamento de Matemáticas Universidad del Cauca Calle 5 No. 4–70 Popayán, Colombia
2Departamento de Matemáticas Universidad del Valle Calle 13 No. 100–00 Cali, Colombia
3School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa
Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 107-118
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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.
DOI : 10.4064/cm140-1-9
Keywords: integer geq k fibonacci sequence which starts ldots terms each term afterwards sum preceding terms paper completes previous work marques which investigated spacing between terms distinct k fibonacci sequences

Jhon J. Bravo  1   ; Carlos A. Gómez  2   ; Florian Luca  3

1 Departamento de Matemáticas Universidad del Cauca Calle 5 No. 4–70 Popayán, Colombia
2 Departamento de Matemáticas Universidad del Valle Calle 13 No. 100–00 Cali, Colombia
3 School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa 
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Jhon J. Bravo; Carlos A. Gómez; Florian Luca. On the distance between
 generalized Fibonacci numbers. Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 107-118. doi: 10.4064/cm140-1-9

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