Curious Generalized Fibonacci Numbers

Author:

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

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⋯ab⋯ba⋯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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference34 articles.

1. The On-Line Encyclopedia of Integer Sequences (OEIS)http://oeis.org

2. Square Curious Numbers;Borade;J. Integer Seq.,2021

3. Fibonacci and Lucas numbers with only one distinct digit;Luca;Port. Math.,2020

4. Repdigits as products of two Fibonacci or Lucas numbers

5. Pell and Pell-Lucas numbers with only one distinct digits;Faye;Ann. Math.,2015

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