Results 11 to 20 of about 4,123,026 (315)

On the properties of k-balancing numbers

Ain Shams Engineering Journal, 2018
In this study, a generalization of the sequence of balancing numbers called as k-balancing numbers is considered and some of their properties are established.
Prasanta Kumar Ray
doaj   +3 more sources

Two Generalizations of Dual-Hyperbolic Balancing Numbers

Symmetry, 2020
In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic k-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.
D. Bród, A. Szynal-Liana, I. Włoch
semanticscholar   +3 more sources

Bidimensional extensions of balancing and Lucas-balancing numbers

Journal of Discrete Mathematical Sciences & Cryptography
In this article bidimensional extensions of balancing and Lucas-balancing numbers are introduced, as well as some properties of these new bidimensional sequences.
Chimpanzo, J., Catarino, Paula, Vasco, Paulo, Borges, Anabela   +3 more
openaire   +3 more sources

A New Identity Involving Balancing Polynomials and Balancing Numbers

Symmetry, 2019
In this paper, a second-order nonlinear recursive sequence M ( h , i ) is studied. By using this sequence, the properties of the power series, and the combinatorial methods, some interesting symmetry identities of the structural properties of balancing ...
Yuanyuan Meng
semanticscholar   +3 more sources

Period of balancing numbers modulo product of consecutive Lucas-balancing numbers

MATHEMATICA, 2018
The period of the balancing numbers modulo m, denoted by π(m), is the least positive integer l such that {Bl, Bl+1} ≡ {0, 1} (mod m), where Bl denotes the l-th balancing number. In the present study, we examine the periods of the balancing numbers modulo
Bijan Kumar Patel, Shanta Kumari Sunanda, Prasanta Kumar Ray   +2 more
openaire   +2 more sources

Balancing Numbers and Application

Journal of Advanced College of Engineering and Management, 2018
 In this paper, we present about origin of Balancing numbers; It!s connection with Triangular, Pells numbers, and Fibonacci numbers; beginning with connections of balancing numbers with other numbers system, It elaborate the different generating functions of balancing numbers.
R. Gautam
openaire   +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.
Rayaguru, Sai Gopal, Panda, Gopal Krishna   +1 more
openaire   +3 more sources

Balancing and Lucas-Balancing Numbers as the Difference of Two Repdigits

13 pages.
Mohapatra, Monalisa, Bhoi, Pritam Kumar, Panda, Gopal Krishna   +2 more
openaire   +4 more sources

Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this work, the general terms of almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers.
Ahmet Tekcan, Esra Zeynep Türkmen
doaj   +1 more source

General Terms of All Almost Balancing Numbers of First and Second Type [PDF]

Communications in Mathematics, 2022
In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first
A. Tekcan, Alper Erdem
semanticscholar   +1 more source