An asymptotic intertwining of the undelayed and delayed Fibonacci numbers

TL;DR

This paper explores the asymptotic relationships between traditional Fibonacci numbers and a new class called Gibonacci numbers, revealing unexpected mutual-bracketing properties that deepen understanding of their mathematical structure.

Contribution

It introduces the Gibonacci numbers and demonstrates their asymptotic interrelation with Fibonacci numbers, expanding the theoretical framework of Fibonacci-related sequences.

Findings

Fibonacci and Gibonacci numbers exhibit mutual-bracketing asymptotic properties

The properties are surprising and extend the understanding of Fibonacci sequences

The results have potential implications in physics and mathematical analysis

Abstract

The list of properties of Fibonacci numbers F(n) (with multifaceted relevance in physics) is complemented by an empirical observation that in combination with the "next" family of the "delayed Fibonacci" numbers G(n) called, for convenience, "Gibonacci numbers" here, both sets exhibit certain remarkable and fairly unexpected asymptotic mutual-bracketing properties.