Results 141 to 150 of about 1,240,504 (163)

Jacobsthal and Jacobsthal-Lucas numbers and sums introduced by Jacobsthal and Tverberg

J. Integer Seq., 2017
Summary: We study the sums introduced by \textit{E. Jacobsthal} [Norske Vid. Selsk. Forhdl. 30, 35--41 (1957; Zbl 0080.26102)] and \textit{H. Tverberg} [Acta Arith. 155, No. 4, 349--351 (2012; Zbl 1276.11011)] and show that the extreme values of the sums are connected with Jacobsthal and Jacobsthal-Lucas numbers.
Kritkhajohn Onphaeng, Prapanpong Pongsriiam   +1 more
openaire   +2 more sources

The Differential Equation in Terms of Jacobsthal and Jacobsthal-Lucas Numbers

2023
Progress in Applied Science and Technology, 13, 1, 1 ...
openaire   +1 more source

Triangular numbers in the Jacobsthal family

Integers, 2012
Summary: Using congruences, second-order Diophantine equations, and linear algebra, we identify Jacobsthal and Jacobsthal-Lucas numbers that are also triangular numbers.
Thomas Koshy, Zhenguang Gao
openaire   +2 more sources

Some new properties of modified Jacobsthal and Jacobsthal-Lucas numbers

AIP Conference Proceedings, 2014
A certain generalization of Jacobsthal numbers was proposed in the form Jns,t = sn-(t)ns+t, where n ≥ 0 is a natural number and s ≠ -t are arbitrary real numbers (Atanassov 2011). As an analogue, a modification of Jacobsthal-Lucas numbers was formulated in the form jns,t = sn+(-t)n, where n is a natural number and s and t are arbitrary real numbers ...
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Jacobsthal numbers and associated Hessenberg matrices

J. Integer Seq., 2018
Summary: In this paper, we define two \(n\times n\) Hessenberg matrices, one of which corresponds to the adjacency matrix of a bipartite graph. We then investigate the relationships between the Hessenberg matrices and the Jacobsthal numbers. Moreover, we give Maple algorithms to verify our results.
Oteles, Ahmet, Karatas, Zekeriya Y., Zangana, Diyar O. Mustafa   +2 more
openaire   +4 more sources

Numerous Determinants Identities Involving Jacobsthal and Jacobsthal Lucas Numbers

Communications on Applied Nonlinear Analysis
Determinants have played an important role in many areas of mathematics. As an example, they are extremely useful in the research and resolution of linear equation and system problems. The study of determinants can be approached from several distinct angles.
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Hyperbolic kk\pmb k-Jacobsthal and kk\pmb k-Jacobsthal-Lucas Quaternions

Indian Journal of Pure and Applied Mathematics, 2021
A D Godase, Mi̇Ne Uysal, Engin Özkan
exaly  

An Introduction to the Jacobsthal Numbers

The College Mathematics Journal, 2023
openaire   +1 more source

A generalization of Collatz functions and Jacobsthal numbers

J. Integer Seq., 2018
Summary: Let \(b\geq 2\) be an integer and \(g = b - 1\). We consider a generalization of the modified Collatz function: for any positive integer \(m\), the \(g\)-Collatz function \(f_g\) divides \(m\) by \(g\), if \(m\) is a multiple of \(g\); otherwise, the \(g\)-Collatz function \(f_g\) is the least integer greater than or equal to \(\frac{bm}{g}\).
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Fibonacci numbers which are products of two Jacobsthal numbers

Tbilisi Mathematical Journal, 2021
Fatih Erduvan, Refik Keskin
exaly