Results 11 to 20 of about 1,598,417 (209)

Boolean Hypercubes, Mersenne Numbers, and the Collatz Conjecture

Journal of Mathematical Sciences and Modelling, 2020
This study is based on the trivial transcription of the vertices of a Boolean \textit{N}-Dimensional Hypercube $\textbf{H}_{N} $ into a subset $\mathbb{S}_{N}$ of the decimal natural numbers $\mathbb{N}.$ Such straightforward mathematical manipulation ...
Ramon Carbó Dorca
doaj   +2 more sources

Global Generalized Mersenne Numbers: Definition, Decomposition, and Generalized Theorems

Symmetry
A new generalized definition of Mersenne numbers is proposed of the form an−a−1n, called global generalized Mersenne numbers and noted GMa,n with base a and exponent n positive integers. The properties are investigated for prime n and several theorems on
Vladimir Pletser
exaly   +2 more sources

BiEntropy, TriEntropy and Primality [PDF]

Entropy, 2020
The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
doaj   +2 more sources

Mersenne numbers as a difference of two Lucas numbers

Commentationes Mathematicae Universitatis Carolinae, 2023
Summary: Let \((L_n)_{n\geq 0}\) be the Lucas sequence. We show that the Diophantine equation \(L_n-L_m=M_k\) has only the nonnegative integer solutions \((n,m,k)=(2,0,1)\), \((3,1,2)\), \((3,2,1)\), \((4,3,2)\), \((5,3,3)\), \((6,2,4)\), \((6,5,3)\) where \(M_k=2^k-1\) is the \(k\)th Mersenne number and \(n>m\).
Alan Murat
semanticscholar   +4 more sources

New Vistas on Mersenne numbers

Proceeding International Conference on Science and Engineering, 2023
Mersenne numbers are analyzed for varieties of interesting properties. Various fascinating relations connecting Mersenne numbers with other special number patterns by means of theorems involving the relations are exhibited.
J. Shanthi, S.Vidhyalakshmi, M. A. Gopalan
semanticscholar   +2 more sources

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Mathematics, 2019
In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit ...
Yunlan Wei, Yanpeng Zheng, Zhaolin Jiang, Sugoog Shon   +3 more
doaj   +2 more sources

Mersenne Numbers in Generalized Lucas Sequences

Proceedings of the Bulgarian Academy of Sciences
Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$
A. Altassan, Murat Alan
semanticscholar   +3 more sources

Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers

Applied Mathematics, 2022
R. Carbó-Dorca
exaly   +2 more sources

The sequence of higher order Mersenne numbers and associated binomial transforms [PDF]

arXiv.org, 2023
In this article, we introduce and study a new integer sequence referred to as the higher order Mersenne sequence. The proposed sequence is analogous to the higher order Fibonacci numbers and closely associated with the Mersenne numbers.
K. Prasad, Munesh Kumari, Rabiranjan Mohanta, H. Mahato   +3 more
semanticscholar   +1 more source

Generalised Mersenne numbers revisited [PDF]

Mathematics of Computation, 2013
32 pages.
Robert Granger, Andrew Moss
openaire   +5 more sources