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Interval Preserving Map Approximation of 3x + 1 Problem

Interval Preserving Map Approximation of 3x + 1 Problem
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The 3x+1 Problem For Rational Numbers : Invariance of Periodic Sequences in 3x+1 Problem

2020 IEEE 14th International Conference on Application of Information and Communication Technologies (AICT), 2020
In the paper, we discuss a generalization of 3x+1 Problem sometimes called Collatz’ (Syracuse) Conjecture. For a given initial rational number, each next number is obtained by dividing the previous integer by 2 (T operation), or multiplying it by 3, adding 1 and then dividing by 2 (S operation), or multiplying by 3, adding 2 and then dividing by 2 (V ...
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Uniform Distribution in the (3x+1)-Problem

Moscow Mathematical Journal, 2003
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THE 3x+1 PROBLEM VIEWED FROM ANOTHER SIDE

JP Journal of Algebra, Number Theory and Applications, 2020
This study concerns the Collatz sequences defined by the recurrence \[ i_{k+1} = \begin{cases} 3i_k+1 & \text{ for }i_k\text{ odd},\\ i_k/2 &\text{ for }i_k\text{ even}\end{cases} \] where the first term \(i_0\) can be any positive integer. It is an open question whether all sequences reach the value 1.
Alaya, J., Atia, M. J., Bouras, B.
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The ``\(3x + 1\)'' problem and finite automata

Bull. EATCS, 1992
Summary: Let \(f(x)=3x+1\) if \(x\) odd, and \(x/2\) if \(x\) even. The ``\(3x+1\)'' conjecture states that for all integers \(n\geq 1\), there exists an \(i\geq 0\) such that \(f^ i(n)=1\). We give a relationship between this famous conjecture and finite automata.
Jeffrey O. Shallit, David A. Wilson
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The \(3x+1\) problem: A quasi cellular automaton

Complex Syst., 1987
The ``Collatz-Ulam-Syracuse-Kakutani'' problem, at its simplest, is the study of the iterates of \(f(x)\) defined equal to \((3x+1)/2\) if x is an odd natural number, and equal to \(x/2\) if \(x\) is an even natural number. Whether \(f\) iterates to 1 is an unresolved issue.
Thomas Cloney, Eric Goles 0001, Gérard Y. Vichniac   +2 more
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On the "3x + 1" Problem

Mathematics of Computation, 1978
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Cancer and the Problem of Pessimism

Ca-A Cancer Journal for Clinicians, 1967
E C Easson
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Advances in Diagnosis and Management of Gastric Cancer: III. The Surgeon and the Problem of Gastric Cancer

Ca-A Cancer Journal for Clinicians, 1957
Owen H Wangensteen
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“Sticky Information” and the Locus of Problem Solving: Implications for Innovation

Management Science, 1994
Eric Von Hippel
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