Results 31 to 40 of about 255,828 (280)

Generalized Fibonacci-Lucas Sequence [PDF]

Turkish Journal of Analysis and Number Theory, 2014
The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field.
Bijendra Singh, Omprakash Sikhwal, Yogesh Kumar Gupta   +2 more
openaire   +1 more source

On Bicomplex Jacobsthal-Lucas Numbers

Journal of Mathematical Sciences and Modelling, 2020
In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and ...
Serpil Halıcı
doaj   +1 more source

Binomial Coefficients and Lucas Sequences

Journal of Number Theory, 2002
Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
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Almost repdigits in balancing and Lucas-balancing sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
doaj   +1 more source

Repdigits in k-Lucas sequences

Proceedings - Mathematical Sciences, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bravo, Jhon J., Luca, Florian
openaire   +1 more source

On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source

Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System [PDF]

, 2000
Study of Smarandache sequences of numbers, and related problems, via a Computer Algebra. Sy::;tem.
Gouveia, Paulo, Torres, Delfim
core   +1 more source

Some properties of the generalized (p,q)- Fibonacci-Like number

MATEC Web of Conferences, 2018
For the real world problems, we use some knowledge for explain or solving them. For example, some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q ...
Suvarnamani Alongkot
doaj   +1 more source

Some Polynomial Sequence Relations

Mathematics, 2019
We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Chan-Liang Chung
doaj   +1 more source

Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source