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The set of rational cycles for the 3x+1 problem [PDF]
Acta Arithmetica, 1990 The notorious ``\(3x+1\)''-problem concerns the behavior under iteration of the function \(T(n)=(3n+1)/2\), \(n\) odd, \(T(n)=n/2\), \(n\) even. The ``\(3x+1\)''-conjecture is the claim that, starting from any positive integer \(n\) the iterates \((n,T(n),T(T(n)),\dots)\) eventually reach the value 1.
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, 2023 The 3x+1 problem asks the following: Suppose we start with a positive integer, and if it is odd then multiply it by 3 and add 1, and if it is even, divide it by 2. Then repeat this process as long as you can. Do you eventually reach the integer 1, no matter what you started with? Collatz conjecture (or 3n+1 problem) has been explored for about 85 years.
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The $3x + 1$ Problem: Two Stochastic Models
The Annals of Applied Probability, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lagarias, J. C., Weiss, A.
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British Journal of Clinical Pharmacology, EarlyView.Aims To determine the prevalence of non‐adherence to antihypertensive medicines and to identify demographic and behavioral factors associated with non‐adherence in subjects enrolled in the May Measurement Month (MMM) 2023, as part of the permanent public health action Hunting the silent killer.
Valerija Bralić Lang +12 more
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Business Strategy and the Environment, EarlyView.ABSTRACT The present study applied the diffusion of innovation theory to investigate the rate of diffusion of renewable energy sources used by Europe's top professional football stadiums and the relationship with carbon neutrality. A discrete diffusion model estimated the diffusion of renewable energy to saturation, and a multivariate logistic ...
Chad S. Seifried +2 more
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CrystalsThe crystal structure of caysichite-(Y) from the Ploskaya Mt (Kola Peninsula, Russia) has been refined to R1 = 0.051 for 4472 unique observed reflections. The mineral is orthorhombic, Ccm21, a = 13.2693(3), b = 13.9455(4), c = 9.7384(2) Å, V = 1802.06(8)
Sergey V. Krivovichev +3 more
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An E-Sequence Approach to the 3x + 1 Problem [PDF]
Symmetry, 2019 For any odd positive integer x, define ( x n ) n ⩾ 0 and ( a n ) n ⩾ 1 by setting x 0 = x , x n = 3 x n − 1 + 1 2 a n such that all x n are odd. The 3 x + 1 problem asserts that there is an x n = 1 for all x.
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The formal proof of 3x+1 problem
, 2023 The Collatz conjecture has been a famous unsolved problem in mathematics for almost a century. This proof is a complete formal proof that can be verified by anyone in the theorem proving support system Coq.
Kobayashi, Teruyuki, Kobayashi, Yoko
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ChemSusChem, Volume 18, Issue 6, March 15, 2025.The product profile of enzymatically hydrolyzed PET can be modified by medium engineering and thereby adapted to a desired product. TPA, MHET or BHET can be forced as the predominant product using a basic pH (blue), 25 % ethylene glycol (EG) and IsPETasewt (green) or ≥25 % EG and LCCICCG (pink), respectively.
Tobias Heinks +8 more
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Dynamique du problème 3x + 1 sur la droite réelle
Ratio Mathematica, 2014 The 3x + 1 problem is a difficult conjecture dealing with quite a simple algorithm on the positive integers. A possible approach is to go beyond the discrete nature of the problem, following M.
Nik Lygeros, Oliveir Rozier
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