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 ...
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 ...
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 $n$ ...
How to write a pseudocode program that halts only if the Collatz Conjecture is false. Thanks much in advance!!!
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 ...
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 ...
What's the importance of multiplying a 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 ...
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 $3n+3$ ...
If somehow one can prove [summation (1/C(x))^2 ] is convergent (or specifically [summation (1/C(x))^2 ]<2e), then can we ...
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 ...