# Questions tagged [collatz-conjecture]

For questions about the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2$ if $n$ is even, and its generalizations.

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### Collatz-esque dynamical problem about prime distribution

I've come up with a scenario which reminds me of the Collatz conjecture in that it's a question about the behavior of a system over time. Let $n=0$ at $t_0$ (i.e. $t=0$). $t$ will increment through ...
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### Is $q\cdot\lvert\cdot\rvert$ a norm?

Let $\lvert x\rvert$ be a ($l^\infty$)norm on a sequence space. Is $q\cdot\lvert x\rvert$ also norm for some positive rational number $q$? This is the motivation for the question: It turns out ...
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### Concept of undecidability and the Collatz problem [duplicate]

I'm reasoning like this: (I don't have enough math education) Suppose that the Collatz Conjecture is undecidable. This means, the Collatz conjecture cannot be proved to be true or false. This means, ...
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### Why problem with simple formulation is so hard?

If you ever heard about Collatz conjecture, you know that it is understandable even for middle school students, but no one has solved it yet. The problem is to prove or to disprove that starting with ...
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### Application of the Collatz conjecture

I'm very curious about the Collatz conjecture, also known as the $3n+1$ problem, mainly due to its rather simple formulation and beautiful visualizations. After all, Erdős himself said that "...
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### Base-10 “reverse pairs” in strings of the iterated Collatz conjecture function.

Details: The following terminology is non-standard. Definition 1: A reverse pair of numbers is a pair of numbers $m$ and $n$ such that, if the decimal expansion of $m$ is \overline{a_1a_2\cdots ...
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### Infinite sets that are proven to be true for Collatz Conjecture?

I know that the set of powers of 2 and the set of 1,5,21,85,341,... are proven to be true for Collatz conjecture. Are there other sets with infinite number of numbers that are also proven to satisfy ...
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### Computational verification of Collatz problem

Every positive integer $n$ can be represented as a product \begin{align} n &= a \cdot 2^k \text{,} \end{align} where the $a$ is odd integer and $k$ is an exponent of two. Let $\varepsilon$ be the ...
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### Is it officially proven that the Collatz sequences can't go to infinity?

Did the mathematician Jeffrey Lagarias prove that in his work the Collatz sequences could not go to infinity (divergent trajectory), that only cyclicity can exist? I don't have enough mathematics to ...
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### On a one formula Collatz function

The top voted answer in Is it possible to describe the Collatz function in one formula? looks like a really complicated function at first sight. Let me restate the function in it's original form here;...