# Tagged Questions

Dynamics of the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2$ if $n$ is even. Generalizations to $n \to 3n-1$ or $n \to 5n+1$ or even to $n \to pn+q$ . Other names are "$3x+1$-problem","syracuse problem". If you have a question, please be specific to your detail. MSE is not ...

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### Collatz Conjecture, sufficient to show odd numbers reach $1$?

The famous conjecture: Let $$f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 3n+1 & \quad \text{if } n \text{ is odd}\\ \end{cases}$$ The Collatz Conjecture ...
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### Collatz Conjecture: Literature on Convergence

Does anyone know of a paper showing that if all n converge, they must converge to unity for n>0. Else, any literature related to convergence properties would be appreciated. Thanks, Jordan
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### Collatz-type problems with known divergent trajectories

It is a well-known problem, known as Collatz problem, to determine whether iteratively applying the map $f(x)=\frac{x}{2}\text{ if$x$is even and }f(x)=3x+1\text{ otherwise}$ on a positive integer $n$...
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### Besides the $3x + 1$ problem, for which similar problems are still unresolved regarding trayectory?

Generalize the $3x + 1$ problem as $cx \pm 1$, where $c$ is a positive odd integer and $x$ is a positive integer iterated through the function as far as possible to discover a cycle. If $x$ is even, ...
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