# 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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### When is a function a permutation of the integers?

When is a function a permutation of the integers? In his 2011 paper on the Collatz conjecture here Lagarias writes; ...
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### Collatz conjecture

See this After seeing this question, I observed first 10 natural numbers , I saw this For every $n\in \mathbb N$ and $n\ne 2^k$ for some $k\in \mathbb N$ , after applying these two operations , ...
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### Collatz conjecture pattern (3n + 1 problem).

I have a pattern I found in Collatz Conjecture I want to share. Afterwards, I would like to know, if I could try harder at this pattern (I am stuck), if it could lead to a proof. Or it would just be ...
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### If the Collatz Conjecture is unsolvable is it true?

Recently Numberphile uploaded a video on Godel's Incompleteness Theorem, and the Professor in the video made the conclusion that if you can prove a statement cannot be proven true or false by the ...
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### Why does the expression $3n+1$ appear in Collatz conjecture?

Why is it important the role of $3n+1$ in Collatz conjecture? I mean, if we replace $3n+1$ by $5n+1$ it seems (numerically) that the modified statement of Collatz conjecture does not hold in this case....
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### Why is this wrong?

About the Collatz Conjecture: Every body looks at it from "leaves to root" - to use the tree analogy. I have another approach. My approach is to look at it from the root - the number 1 - and see if, ...
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About the Collatz conjecture: Let Steps be: Number of steps, S, that a "counting number", n, takes to reach 1 - sometimes referred as the stopping time (of n); Example: 5 take 5 steps to reach 1 (...
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### In the Collatz conjecture, why are $\max(\textrm{collatz}(n))$ and $\textrm{var}(\textrm{collatz}(n))$ so closely related?

Like the question title reads, in the Collatz conjecture, why are $\max(\textrm{collatz}(n))$ and $\textrm{var}(\textrm{collatz}(n))$ so closely related? See the Figure below for a log-log plot. I ...
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### How many “non-Collatz-numbers” do exist?

Everybody knows or at least heard about Collatz or $3x+1$ conjecture. Let us now define something like: Definition 1: Number $m \in \mathbb{N}$ is called $k-Collatz$ number if in its sequence ...
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### What is the latest verified research on the 3x+1 Problem? [closed]

Wikipedia : Collatz Conjecture Take any positive integer n. If n is even, divide it by $2$ to get $n / 2$. If n is odd, multiply it by $3$ and add $1$ to obtain $3n + 1$. Repeat the process (which ...
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### Can there exist such a Collatz cycle that never divides by 2 more than one time between the increasing parts?

Sorry for the long title. I first of all want to say that I'm just a high school student who spent today looking into the Collatz conjecture. I, first of all, would like to know if it's known whether ...
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### Is there a proof for this modified Collatz-like problem?

The Collatz Conjecture is a famously unproven problem in mathematics, but I was thinking of a slight modification, and whether or not a proof of this different form is trivial. Here is a statement of ...
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### Property unique to Collatz?

Just an amateur having fun with some sequences and would like to understand what I'm seeing. Playing with Collatz in python and found something interesting when I plotted the following: Where I plot ...
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### Smallest number of a hypothetical second Collatz Cycle

Most here are probably aware of the Collatz Conjecture. It is conjectured that every number eventually ends in a trivial cycle of 1 -> 4 -> 2 -> 1 if you follow these rules: Take any number: If it ...
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### Find an infinite sequence of statements so that truthness of all sequence elements is unprovable

Let us consider a function $f: \mathbb N \to \left\{0, 1\right\}$ with finite description length (i.e. describable by a finite length program for a Turing machine) satisfying the following conditions: ...
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### The connection between the Collatz Conjecture and the Optic Equation

The Collatz Conjecture is fun for those of us who have never taken mathematics in university in any meaningful way. It's also probably fun for all of you who have gone to university. So I want to ...
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### Collatz Number System Question

I was looking at the Collatz Conjecture and I thought of something: If we denote two operators $a_n = 2n$ and $b_n = \frac{n-1}{3}$, then every number that converges using the Collatz Conjecture can ...
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### Does $\frac{(3x+1)}{2^n}$ generate a partial ordering of the odd, positive integers?

Taking $n,m\in\mathbb{N}$ and $n,m >0$ throughout. Does the graph of the function $f(x)=\frac{(3x+1)}{2^n}$ generate a partial ordering of the odd integers? Because if it did, it would seem to me ...
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### Intuition behind lack of cycles in the Collatz Conjecture

The Collatz Conjecture concerns the function $f(n) = \begin{cases} n/2, & \text{if$n$is even} \\ 3n+1, & \text{if$n$is odd} \end{cases}$ . The conjecture says that if you start with ...
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### The square of every prime number can be expressed in a linear form. [duplicate]

While working on the Collatz conjecture, I've found that the square of every prime number $p$ (except 2 and 3)can be written in the form of $12k+1$. $p^2=12k+1$.$(k\in\mathcal N)$ is this a new ...
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### Is this a proof of the Collatz Conjecture?

I recently stumbled upon the following paper from April 2016: https://www.researchgate.net/publication/299749569_A_proof_of_the_Collatz_conjecture Its researchers, who are university professors, ...
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