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Displaying similar documents to “Differences of multiple Fibonacci numbers.”

An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.

On terms of linear recurrence sequences with only one distinct block of digits

Diego Marques, Alain Togbé (2011)

Colloquium Mathematicae

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In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.

The Geometric and Dynamic Essence of Phyllotaxis

P. Atela (2011)

Mathematical Modelling of Natural Phenomena

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We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.

Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Ahmet Daşdemir (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.

An exercise on Fibonacci representations

Jean Berstel (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.