Curious Generalized Fibonacci Numbers

Jose L. Herrera, Jhon J. Bravo and Carlos A. Gómez
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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

Mathematics, 2021, vol. 9, issue 20, 1-12

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.

Keywords: generalized Fibonacci number; repdigit; linear form in logarithms; reduction method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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