Results 1 to 10 of about 1,598,398 (191)

On generalized bihyperbolic Mersenne numbers [PDF]

Mathematica Bohemica, 2023
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
doaj   +3 more sources

On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
doaj   +3 more sources

Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]

PLoS ONE, 2023
An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov, Yelizaveta S Vitulyova, Dinara K Matrassulova   +2 more
doaj   +2 more sources

On the Number of Divisors of Mersenne Numbers [PDF]

Experimental Mathematics
Denote $f(n):=\sum_{1\le k\le n} \tau(2^k-1)$, where $\tau$ is the number of divisors function. Motivated by a question of Paul Erd\H{o}s, we show that the sequence of ratios $f(2n)/f(n)$ is unbounded.
Vjekoslav Kovavc, Florian Luca
semanticscholar   +3 more sources

On New Sequences of $p$-Binomial and Catalan Transforms of the $k$-Mersenne Numbers and Associated Generating Functions

Universal Journal of Mathematics and Applications
In this work, we investigate the binomial transforms and Catalan transform of the $k$-Mersenne and $k$-Mersenne-Lucas numbers and examine the new integer sequences.
Kalika Prasad, Hrishikesh Mahato, Ritanjali Mohanty, Munesh Kumari   +3 more
doaj   +2 more sources

Fermat and Mersenne numbers in $k$-Pell sequence

Математичні Студії, 2021
For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
doaj   +2 more sources

ON GAUSSIAN MERSENNE NUMBERS

Journal of Science and Arts, 2021
In this paper, we define Gaussian Mersenne numbers and we give some properties of them. Moreover we present some relations among Gaussian Mersenne numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal-Lucas numbers.
D. Taşcı
semanticscholar   +2 more sources

On the Eight Levels theorem and applications towards Lucas-Lehmer primality test for Mersenne primes, I

Arab Journal of Basic and Applied Sciences, 2023
Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy.
Moustafa Mohamed
exaly   +3 more sources

Gaussian Mersenne numbers and generalized Mersenne quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2019
In this study, we introduce a new class of quaternions associated with the well-known Mersenne numbers. There are many studies about the quaternions with special integer sequences and their generalizations.
Ahmet Daşdemir, Göksal Bilgici
semanticscholar   +2 more sources

Learned pseudo-random number generator: WGAN-GP for generating statistically robust random numbers. [PDF]

PLoS ONE, 2023
Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary ...
Kiyoshiro Okada, Katsuhiro Endo, Kenji Yasuoka, Shuichi Kurabayashi   +3 more
doaj   +2 more sources