Research Article

k−Fibonacci numbers close to a power of 2

Published in: Quaestiones Mathematicae
Volume 44 , issue 12 , 2021 , pages: 1681–1690

DOI: 10.2989/16073606.2020.1818645

Author(s): Jhon J. Bravo , Colombia , Carlos A. Gómez , Colombia , Jose L. Herrera , Colombia

Keywords: 11B39 , 11J86 , 11B39 , 11J86

Abstract

A generalization of the well-known Fibonacci sequence is the k-generalized 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, by using a lower bound to linear forms in logarithms of algebraic numbers due to Matveev and some argument of the theory of continued fractions, we find all the members of F ^(k) which are close to a power of 2. This paper continues and extends the previous work of Chern and Cui which investigated the Fibonacci numbers close to a power of 2.

« A two-variable Dirichlet series and its applications

Multivalued generalized graphic θ-contraction on directed graphs and application to mixed Volterra-Fredholm integral inclusion equations »