Results 31 to 40 of about 141 (103)
Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach
IEEE AccessThe Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics.
Eyob Solomon Getachew +1 more
doaj +1 more source
Some considerations on the total stopping time for the Collatz problem
Vojnotehnički GlasnikIntroduction/purpose: The Collatz conjecture has been considered and the stopping time needed for the recursive transformation to end has been investigated. Methods: A statistical analysis on the stopping time has been used.
Nicola Fabiano +2 more
doaj +1 more source
International Journal of Mathematics and Mathematical Sciences, 2020 We propose reduced Collatz conjecture and prove that it is equivalent to Collatz conjecture but more primitive due to reduced dynamics. We study reduced dynamics (that consists of occurred computations from any starting integer to the first integer less ...
Wei Ren
doaj +1 more source
Discrete Mathematics & Theoretical Computer Science, 2002 We use Conway's \emphFractran language to derive a function R:\textbfZ^+ → \textbfZ^+ of the form R(n) = r_in if n ≡ i \bmod d where d is a positive integer, 0 ≤ i < d and r_0,r_1, ...
Kenneth G. Monks
doaj +1 more source
On the Probabilistic Proof of the Convergence of the Collatz Conjecture
Journal of Probability and Statistics, 2019 A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by 2 that follows a recurrent pattern of the form x,1,x,1…, where x ...
Kamal Barghout
doaj +1 more source
A Generalized Resource‐Constrained Framework for Quantifying Ecosystem Water and Carbon Fluxes
Water Resources Research, Volume 62, Issue 6, June 2026.Abstract Gross primary productivity (GPP) and evapotranspiration (ET) represent two fundamental processes in coupled water and carbon cycles. The strong regulation of ecosystem carbon and water fluxes by stomata is well understood at the leaf level. However, the coupling is complex at regional or ecosystem scales.
Shuai Wang +8 more
wiley +1 more source
, 2023 This 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.
openaire +1 more source
Recursive sufficiency for the Collatz conjecture and computational verification [PDF]
Notes on Number Theory and Discrete MathematicsWe define the notion of recursive sufficiency for the Collatz conjecture and we use it to present some results concerning the computational verification of the conjecture.
Mohammad Ansari
doaj +1 more source
Diversity and Distributions, Volume 32, Issue 4, April 2026.ABSTRACT Aim Grasses comprise three main photosynthetic pathway variants (C3‐BOP, C3‐PACMAD and C4‐PACMAD hereafter referred to as C4). We sought to confirm climate niche differences among these photosynthetic pathway variants and assessed whether predicted non‐native grass range shift patterns with climate change differ among photosynthetic pathway ...
Curtis C. Daehler +4 more
wiley +1 more source
Asian Research Journal of Mathematics, 2019 Collatz conjecture (stated in 1937 by Collatz and also named Thwaites conjecture, or Syracuse, 3n+1 or oneness problem) can be described as follows: Take any positive whole number N. If N is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process to the result over and over again.
openaire +2 more sources