On Concatenations of Two k -Generalized Fibonacci Numbers

2024/05/23 by Altassan, Alaa, Alan, Murat · 1 citation
#11B39 #11D61 #11J86 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2405.15001

Abstract

Let k ≥ 2 be an integer. The k- generalized Fibonacci sequence is a sequence defined by the recurrence relation F_n^(k)=F_n-1^(k) + ⋯ + F_n-k^(k) for all n ≥ 2 with the initial values F_i^(k)=0 for i=2-k, …, 0 and F₁^(k)=1. In 2020, Banks and Luca, among other things, determined all Fibonacci numbers which are concatenations of two Fibonacci numbers. In this paper, we consider the analogue of this problem by taking into account k-generalized Fibonacci numbers as concatenations of two terms of the same sequence. We completely solve this problem for all k ≥ 3.

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