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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8answers
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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 ...
14
votes
3answers
664 views
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 $n$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
3
votes
2answers
80 views
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 ...
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 ...
2
votes
3answers
252 views
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 ...
1
vote
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 ...
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 ...
1
vote
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 ...
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
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 $3n+3$ ...
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!!!
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 ...
0
votes
1answer
1k views
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:
...
0
votes
0answers
24 views
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 ...
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votes
1answer
204 views
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 ...
