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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2answers
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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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1answer
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Have 3n + 1 Problem Proof --But can't do the Mathspeak [closed]
I've come here as a last resort. When I first saw the Collatz conjecture I worked out pretty quickly what the dynamic was that drove the Collatz sequences.
That was in 2009. Since then I've been ...
46
votes
8answers
8k views
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 ...
7
votes
3answers
710 views
What does proving the Collatz Conjecture entail?
From the get go: i'm not trying to prove the Collatz Conjecture where hundreds of smarter people have failed. I'm just curious.
I'm wondering where one would have to start in proving the Collatz ...
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1answer
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What does the right arrow mean in the example provided.
My second question here. Does it show that I know very little about mathematics? :)
I'm doing Project Euler Question 14 and would like to know what the right arrow → means in:
...
8
votes
1answer
345 views
What are possibilities to disprove the Collatz Conjecture?
I was thinking about the Collatz Conjecture yesterday, and as opposed to trying to prove it, I was considering what would make the conjecture false. There were only two cases I could think of:
We ...
8
votes
1answer
352 views
Thoughts on the Collatz conjecture; integers added to powers of 2
I've had a thought about the Collatz conjecture (the 3n+1 problem).
Suppose some number, C, diverges under the iteration. We first note that C must be odd because if C were even it would be halved ...
14
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3answers
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The $5n+1$ Problem
The Collatz Conjecture is a famous conjecture in mathematics that has lasted for over 70 years. It goes as follows:
Define $f(n)$ to be as a function on the natural numbers by:
$f(n) = n/2$ if $n$ ...
4
votes
2answers
243 views
Probability and the Collatz Problem
A long time ago I was messing around with the Collatz problem and I stumbled across a "proof" that the iterations will converge. I was too embarrassed to show anyone, and I recently just remembered ...
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4answers
402 views
Collatz Conjecture exclusivity
I have been wondering if there are any numbers that exist only in their own string of the 3n+1 problem.
I need to explain that better. Basically, when you follow the rules of the conjecture, you end ...
0
votes
2answers
500 views
What to do with Collatz proof? [closed]
I have discovered a proof solving the Collatz problem, and I have no idea what to do with it. Given the nature of the topic, all the experts I've found that are capable of reviewing the paper ...
4
votes
1answer
266 views
Required reading on the Collatz Conjecture
I am currently writing a paper on 3x+1 and realized that despite having enough knowledge to work on a singular facet of the problem I lack a more broad understanding of the problem. I have seen the ...
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votes
3answers
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Is this statement stronger than the Collatz conjecture?
$n$,$k$, $m$, $u$ $\in$ $\Bbb N$;
Let's see the following sequence:
$x_0=n$; $x_m=3x_{m-1}+1$.
I am afraid I am a complete noob, but I cannot (dis)prove that the following implies the ...
3
votes
2answers
200 views
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 ...
1
vote
1answer
203 views
Converse of Collatz Conjecture
How to write a pseudocode program that halts only if the Collatz Conjecture is
false.
Thanks much in advance!!!
1
vote
3answers
269 views
Ways of disproving proofs of the Collatz Conjecture?
I jokingly suggested for someone to prove the Collatz Conjecture, and they came up with their own proof. I have no idea how to disprove proofs, so can anyone tell me either what is wrong with this ...
1
vote
3answers
274 views
$5n+1$, $3n-1$ problem, smallest repeating cycle and Collatz conjecture
Among the Collatz conjecture we have other "similar" problems that are solved and have repeating cycles.
$5n+1$ has the repeating cycle $13, 66, 33, 166, 83, 416, 208, 104, 52, 26$, with a length of ...
1
vote
2answers
169 views
$N \equiv 3 (\textrm{mod } 4)$ and Collatz conjecture
Can the Collatz conjecture also be interpreted as behaviour, transformation of number of form $N\equiv 3(\textrm{mod }4)$ to the form of $N\equiv 1(\textrm{mod }4)$
Because integers of the form ...
0
votes
0answers
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Generating sequences with specific characteristics
We are all familiar with pseudo-random sequences generated by various methods (BBS, Mersenne Twister, LCG, Von Neumann's middle square, RC4) and also the 'pseudo-random' sequence of powers of a ...
4
votes
2answers
104 views
How many ways to reach $1$ from $n$ by doing $/13$ or $-7$?
How many ways to reach $1$ from $n$ by doing $/13$ or $-7$ ?
(i.e., where $n$ is the starting value (positive integer) and $/13$ means division by $13$ and $-7$ means subtracting 7)?
Let the number ...
1
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1answer
331 views
What is known about Collatz like 3n + k?
I wonder what is known about variations of Collatz where $3n+1$ is replaced by $3n + 2k + 1$ where k is a fixed positive integer. In the OP ' about Collatz $3n+3$ ' it was confirmed that $3n+3$ ...
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2answers
358 views
About Collatz 3n+3?
While trying to prove the Collatz conjecture I came across the following Lemma :
Lemma $1$ :
All variables are positive integers.
Define $Collatz(n)$ as the result of the (repeated) collatz ...
