Results 41 to 50 of about 1,804,204 (295)

Fibonacci Numbers with a Prescribed Block of Digits

Mathematics, 2020
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from Diophantine ...
P. Trojovský
semanticscholar   +1 more source

New Properties and Identities for Fibonacci Finite Operator Quaternions

Mathematics, 2022
In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions.
Nazlıhan Terzioğlu, Can Kızılateş, Wei-Shih Du   +2 more
doaj   +1 more source

Closed Formulas for the Sums of Squares of Generalized Fibonacci Numbers

, 2020
In this paper, closed forms of the sum formulas for the squares of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +1 more source

On New Formulas of Fibonacci and Lucas Numbers Involving Golden Ratio Associated with Atomic Structure in Chemistry

Symmetry, 2021
The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the golden ratio, the Lucas numbers, and other special numbers.
Rifat Battaloğlu, Y. Simsek
semanticscholar   +1 more source

Periodic words connected with the Fibonacci words

Karpatsʹkì Matematičnì Publìkacìï, 2016
In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and investigated their properties.
G.M. Barabash, Ya.M. Kholyavka, I.V. Tytar   +2 more
doaj   +1 more source

Some identities for generalized Fibonacci and Lucas numbers

AKCE International Journal of Graphs and Combinatorics, 2020
In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana, Iwona Włoch, Mirosław Liana   +2 more
doaj   +1 more source

Curious Generalized Fibonacci Numbers

Mathematics, 2021
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.,
Jose L. Herrera, Jhon J. Bravo, Carlos A. Gómez   +2 more
doaj   +1 more source

Generalized Fibonacci Numbers: Sum Formulas

Journal of Advances in Mathematics and Computer Science, 2020
In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +1 more source

On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3 [PDF]

International Journal of Number Theory, 2019
For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term afterwards is the sum of the ...
M. Ddamulira, F. Luca
semanticscholar   +1 more source

On Distance (r,k)-Fibonacci Numbers and Their Combinatorial and Graph Interpretations

Journal of Applied Mathematics, 2015
We introduce three new two-parameter generalizations of Fibonacci numbers. These generalizations are closely related to k-distance Fibonacci numbers introduced recently. We give combinatorial and graph interpretations of distance (r,k)-Fibonacci numbers.
Dorota Bród
doaj   +1 more source