Results 11 to 20 of about 141 (103)
Scale-free behavior in hailstone sequences generated by the Collatz map
Physical Review Research, 2021 The Collatz conjecture, perhaps the most elementary unsolved problem in mathematics, claims that for all positive integers n, the map n↦n/2 (n even) and n↦3n+1 (n odd) reaches 1 after a finite number of iterations.
M. G. E. da Luz +3 more
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About two countable families in the finite sets of the Collatz Conjecture
Ratio Mathematica, 2021 With t∊ℕ we define the sets Kt and Kt*containing all positive integers that converge to 1 in t iterations in the form of Collatz algorithm. The following are the properties of the { Kt }t∊ℕ and { Kt* }t∊ℕ : countability, empty intersection between the
Michele Ventrone
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Modified Collatz conjecture or (3a + 1) + (3b + 1)I Conjecture for Neutrosophic Numbers 〈Z ∪ I〉 [PDF]
Neutrosophic Sets and Systems, 2016 In this paper, a modified form of Collatz conjecture for neutrosophic numbers is defined.
W. B. Vasantha Kandasamy +2 more
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Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture
Journal of Mathematical Sciences and Modelling, 2022 Using simple arguments derived from the Boolean hypercube configuration, the structure of natural spaces, and the recursive exponential generation of the set of natural numbers, a linear classification of the natural numbers is presented.
Ramon Carbó Dorca, Carlos Perelman
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Novel Theorems and Algorithms Relating to the Collatz Conjecture
International Journal of Mathematics and Mathematical Sciences, 2021 Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof.
Michael R. Schwob +2 more
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Almost all orbits of the Collatz map attain almost bounded values
Forum of Mathematics, Pi, 2022 Define the Collatz map ${\operatorname {Col}} \colon \mathbb {N}+1 \to \mathbb {N}+1$ on the positive integers $\mathbb {N}+1 = \{1,2,3,\dots \}$ by setting ${\operatorname {Col}}(N)$ equal to $3N+1$ when N is odd and $N/2$
Terence Tao
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A Conjecture Equivalent to the Collatz Conjecture
CoRR, 2021 We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
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The structure of the 3x + 1 problem
Electronic Journal of Graph Theory and Applications, 2021 Paul Erdös said about the 3x+1 problem, "Mathematics is not yet ready for such problems". And he is seemingly right. Although we cannot solve this problem either, we provide some results about its structure.
Alf Kimms
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Proof of the Collatz Conjecture
Theoretical Mathematics & Applications, 2022 Abstract The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture.
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Understanding Collatz Conjecture
SSRN Electronic Journal, 2023 <p>This paper is about understanding Collatz conjecture in hailstone numbers.</p>
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