Results 121 to 130 of about 1,995,314 (144)

Balancing and Lucas-balancing numbers which are concatenation of three repdigits

Boletin De La Sociedad Matematica Mexicana, 2023
Let \((B_n)_{n\geq 0}\) be sequence A001109 and \((C_n)_{n\geq 0}\) be sequence A001541 in OEIS. Both sequences have the same characteristic polynomial \(x^2-6x+1\). We have \[B_n=\frac{\alpha^n-\beta^n}{4\sqrt{2}}\mbox{ and }C_n=\frac{\alpha^n+\beta^n}{2}\] for all \(n\geq0\), where \(\alpha=3+2\sqrt{2}\) resp.
Jhon Jairo Bravo Grijalba, Sai Gopal Rayaguru   +1 more
exaly   +2 more sources

Repdigits as Products of Consecutive Balancing or Lucas-Balancing Numbers

The Fibonacci Quarterly, 2018
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive balancing or Lucas-balancing numbers.
Sai Gopal Rayaguru
exaly   +3 more sources

Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers

The Journal of the Indian Mathematical Society, 2022
In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.
Rayaguru, S. G., Panda, G. K.
openaire   +2 more sources

Exact Divisibility by Powers of the Balancing and Lucas-Balancing Numbers

The Fibonacci Quarterly, 2021
Asim Patra
exaly   +2 more sources

On the Periodicity of Lucas-Balancing Numbers and p-adic Order of Balancing Numbers

Iranian Journal of Science and Technology, Transaction A: Science, 2020
The objective of this article is to study the periodicity of Lucas-balancing numbers modulo any positive integer. Some relations between the periodicity of balancing and Lucas-balancing numbers are also discussed. Further, in this study the p-adic order of balancing numbers is completely characterized .
Takao Komatsu, Bijan Kumar Patel
exaly   +2 more sources

Diophantine equations concerning balancing and Lucas balancing numbers

Archiv Der Mathematik, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sudhansu Sekhar Rout, Pallab Kanti Dey
exaly   +3 more sources

On the Properties of Lucas-Balancing Numbers by Matrix Method

Sigmae, 2014
Balancing numbers n and balancers r are originally dened as the solution of the Diophantine equation 1 + 2 + ... + (n - 1) = (n + 1) + (n + 2) + ... + (n + r). If n is a balancing number, then 8n^2 +1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n^2 + 1 is called a Lucas-balancing number.
openaire   +1 more source

Octonions and hyperbolic octonions with the k-balancing and k-Lucas balancing numbers

Journal of Analysis
In this paper, the authors defined the \(k\)-balancing and \(k\)-Lucas balancing octonions and hyperbolic octonions. For \(n\geq 0\), the \(n^{th}\) \(k\)-balancing octonions \(\{B\mathbb{Q}_{k,n}\}\) and the \(n^{th}\) \(k\)-Lucas balancing octonions \(\{C\mathbb{Q}_{k,n}\}\) are defined \[ B\mathbb{Q} _{k,n}=B_{k,n}e_{0}+B_{k,n+1}e_{1}+B_{k,n+2}e_{2}+
Jagmohan Tanti, Kalika Prasad, Munesh Kumari   +2 more
exaly   +2 more sources

Balancing and Lucas-Balancing hybrid numbers and some identities

Journal of Information and Optimization Sciences
In this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them. In addition, we find Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, exponential generating
Mine Uysal, Engin Özkan
openaire   +1 more source

Spinor algebra of k-balancing and k-Lucas-balancing numbers

Journal of Algebra and Its Applications
In this paper, we introduce and study a spinor algebra of [Formula: see text]-balancing numbers referred to as the [Formula: see text]-balancing and [Formula: see text]-Lucas-balancing spinors. First, we give [Formula: see text]-balancing quaternions and their some algebraic properties. Then we introduce a spinor family of [Formula: see text]-balancing
Kalika Prasad, Munesh Kumari, Ritanjali Mohanty, Hrishikesh Mahato   +3 more
openaire   +1 more source