# 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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### What is the importance of the Collatz conjecture?

I have been fascinated by this problem since I first heard about it in high school. From the Wikipedia article http://en.wikipedia.org/wiki/Collatz_problem: Take any natural number $n$. If $n$ is ...
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### Why is $3$ the multiplicative coefficient in the Collatz conjecture?

What's the importance of multiplying an odd number by $3$ and adding $1$, instead of just adding $1$? After all, if you add $1$ to an odd number then it turns into an even number. Here is a example ...
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### The nonexistence of the Collatz-“1-cycle” by an elementary proof - am I missing something?

The so-called "1-cycle" in the Collatz-problem was already disproved by Ray Steiner 1977. However, he used transcendental number theory to achieve that, and Lagarias commented, it is surprising that ...
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### Is this property of the Collatz sequence interesting?

As an amateur playing around with the Collatz conjecture, I've stumbled on something I haven't seen mentioned before, and that may or may not be noteworthy. Suggested by Gottfried Helms, here's a ...
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### Partitions of the odd integers

Understanding the nature of the odd integers is a necessity to prepare oneself to work on the unsolved problems in number theory, such as the Collatz $3n+1$ problem. I hope to demonstrate how the ...
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### What are some reasonable things to prove about the Collatz Conjecture?

I am writing an undergraduate paper on the $3n+1$ problem, and I am looking for some theorems related to the problem that would be reasonable for someone with my mathematical background to prove. I'm ...
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### How is this fractal produced?

It is stated here: Iterating the above optimized map $$f(z)=\frac{1}{4}(1 + 4z - (1 + 2z)\cos(\pi z))$$in the complex plane produces the Collatz fractal. The point of view of iteration on ...
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### A general question about the Collatz Conjecture and finding that integer that doesn't work

I apologize if this question gets down-voted ahead of time. I've been working on the Collatz Conjecture all day with Python, because that is the language I'm most familiar with (I'm not a CS student, ...
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I worked on the Collatz conjecture extensively for fun and practise about a year ago (I'm a CS student, not mathematician). Today, I was browsing the Project Euler webpage, which has a question ...
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### Has the Collatz Conjecture been proven to be unprovable? [closed]

This paper, from a peer-reviewed journal, purports to prove that the Collatz Conjecture is unprovable. If itâ€™s valid, why has it not received more attention? If itâ€™s invalid, what is the flaw, and ...
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### Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

For what values of $m,n$ natural, do $2^n - 1$ is divisible by $2^{m+n} - 3^m$? Thank you very much.
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### How could Collatz conjecture possibly be undecidable?

I wonder how the collatz conjecture could possibly be undecidable? Since let's say it's undecidable, then that means that no counter example can ever be found, and that to me seems to imply that non ...
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### Prerequisite reading before studying the Collatz $3x+1$ Problem

Let's assume I am starting college and have just finished calculus. I've been reading a bit online about the Collatz $3x+1$ Problem and find it to be very intriguing. However, a lot of what I'm ...
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### Examples of “eventually reaches y under iteration” other than the Collatz problem

The Collatz conjecture states that iteratively applying the map $$f(n) = \begin{cases} n/2 &\text{if } n \equiv 0 \pmod{2}\\ 3n+1 & \text{if } n\equiv 1 \pmod{2} .\end{cases}$$ to any ...
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### Collatz cycle necessary condition.

Has it been established that a nontrivial m-cycle of the Collatz conjecture on the positive integers would require two consecutive raises (i.e., if $\{x_1, x_2, \ldots x_n\}$ is the odd positive ...
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### arithmetic sequence $8n+1$ and the collatz conjecture
Is it a known result that if for all $n$ the collatz sequence of $8n+1$ lead to $1$, all natural numbers will?