Results 1 to 10 of about 141 (103)
Some of the next articles are maybe not open access.
Efficient Exhaustive Verification of the Collatz Conjecture using DSP blocks of Xilinx FPGAs
International Journal of Networking and Computing, 2011Yasuaki Itô, Koji Nakano
exaly
PROOFThis paper presents an analysis of the number of zeros in the binary representation of natural numbers. The primary method of analysis involves the use of the concept of the fractional part of a number, which naturally emerges in the determination of binary representation.
Asset Durmagambetov +1 more
+34 more sources
Encrypted audio dataset based on the Collatz conjecture. [PDF]
Data Brief, 2019 In information security, one way to keep a secret content is through encryption. The objective is to alter the content so that it is not intelligible, and therefore only the intended user can reveal the secret content. With the aim to provide examples of
Renza D, Mendoza S, Ballesteros L DM.
europepmc +2 more sources
Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method
Mathematics, 2022 In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can ...
Mercedes Orús-Lacort +1 more
exaly +3 more sources
A Clustering Perspective of the Collatz Conjecture
Mathematics, 2021 This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive ...
J A Tenreiro Machado +2 more
exaly +3 more sources
A Novel Image Encryption Scheme Based on Collatz Conjecture. [PDF]
Entropy (Basel), 2018 Image encryption methods aim to protect content privacy. Typically, they encompass scrambling and diffusion. Every pixel of the image is permuted (scrambling) and its value is transformed according to a key (diffusion). Although several methods have been
Ballesteros DM, Peña J, Renza D.
europepmc +2 more sources
Reduced Collatz Dynamics Data Reveals Properties for the Future Proof of Collatz Conjecture
Data, 2019 Collatz conjecture is also known as 3X + 1 conjecture. For verifying the conjecture, we designed an algorithm that can output reduced dynamics (occurred 3 × x + 1 or x/2 computations from a starting integer to the first integer smaller than the ...
Wei Ren
exaly +3 more sources