Results 221 to 230 of about 51,391 (253)

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 J Bravo, Sai Gopal Rayaguru, Bravo Jhon J   +2 more
exaly   +3 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, Komatsu Takao   +2 more
exaly   +3 more sources

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

The Fibonacci Quarterly, 2021
Asim Patra
exaly   +3 more sources

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}+
Kalika Prasad, Munesh Kumari, Jagmohan Tanti   +2 more
exaly   +3 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.
S. G. Rayaguru, G. K. Panda
semanticscholar   +3 more sources

Balancing and Lucas-balancing numbers as difference of two repdigits

Positive integers with all digits equal are called repdigits. In this paper, we find all balancing and Lucas-balancing numbers, which can be expressed as the difference of two repdigits.
M. Mohapatra, P. K. Bhoi, Gopal Krishna Panda   +2 more
semanticscholar   +5 more sources

Diophantine equations concerning balancing and Lucas balancing numbers

Archiv Der Mathematik, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pallab Kanti Dey, Sudhansu Sekhar Rout
exaly   +4 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.
S. G. Rayaguru, G. K. Panda
semanticscholar   +3 more sources

A note on the generalized bi-periodic Lucas-balancing numbers

BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS
In this study, we introduce a new class of integers called the sequence of generalized bi-periodic Lucas-balancing numbers, which extends the well-known sequence of Lucas-balancing numbers.
E. A. Costa, E. Spreafico, P. Catarino
semanticscholar   +2 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.
P. Ray
semanticscholar   +2 more sources