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MASHMATICS: A Unified Continuous Framework for Collatz-Type Iterative Functions
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Some Holomorphic Functions connected with the Collatz Problem
Some Holomorphic Functions connected with the Collatz Problemopenaire
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Multiplication Algorithm Based on Collatz Function
Theory of Computing Systems, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Barina, Barina David
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Functional Equations Connected With The Collatz Problem
Results in Mathematics, 1994The still open \(3x+1\)-problem (or Collatz- or Hasse- or Syracuse- or Kakutani-problem) is to prove that for every \(n\in \mathbb{N}\) there exists a \(k\) with \(t_ k(n)= 1\) where the function \(t(n)\) takes odd numbers \(n\) to \((3n+1)/2\) and even numbers \(n\) to \(n/2\) and the iterates of this mapping are defined recursively by \(t_ 0(n) =n\),
Berg, Lothar, Meinardus, Günter
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A generalization of Collatz functions and Jacobsthal numbers
J. Integer Seq., 2018Summary: Let \(b\geq 2\) be an integer and \(g = b - 1\). We consider a generalization of the modified Collatz function: for any positive integer \(m\), the \(g\)-Collatz function \(f_g\) divides \(m\) by \(g\), if \(m\) is a multiple of \(g\); otherwise, the \(g\)-Collatz function \(f_g\) is the least integer greater than or equal to \(\frac{bm}{g}\).
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From Collatz Conjecture to Hash Function
2023Masrat Rasool, Samir Brahim Belhaouari
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Pseudo-random number generators based on the Collatz conjecture
International Journal of Information Technology (Singapore), 2019Dan E Tamir
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The Collatz conjecture and De Bruijn graphs
Indagationes Mathematicae, 2013Thijs Laarhoven, Benne De Weger
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On a Lattice Collatz Function with Nontrivial Cycles
Albertin, Erin T +2 moreopenaire +1 more source