collatz conjecture Definition and 18 Threads

These are the two tables I developed trying to untangle how the Collatz Conjecture operates, and this certainly helps clear the water a bit

I did a study of the Collatz conjecture and found that all even numbers can be removed from the Collatz conjecture because even numbers act as the connecting links between odd numbers. What do you think about it? Is it a breakthrough in 3n+1 problem? 27 -> 41 -> 31 -> 47 -> 71 -> 107 -> 161 ->...

Note as soon as the term 3N+1 become divisible by a power of 2 we can repeatedly divide by 2. For the proof below we rearrange the sequence so it becomes: First step: If N is odd, multiply by 3 and add 1. Each next step: - Repeatedly divide by 2, as many times as the number k, which is...

The Collatz problem is perhaps the only unsolved math problem I actually understand. It "feels" like a proof would be trivial, though obviously it isn't. Been playing with different variations in hopes of understanding it better. Is it a set problem (proving there's no intersection between two...

Can this proposition be proved and become a lemma in the proof of Collatz conjecture? $$collatz(n) \geq \lfloor \frac{log(n)}{log(2)} \rfloor.$$

I have been interested in the attempts to prove this Conjecture since 2000 and like many others (eg Ken Conrow) I have tried to find a convincing solution. Today I read on this forum what looks like a proof that there cannot be an internal cycle beyond 4:2:1 but I don't think the author realizes...

There is a graph showing n on its x-axis and its total stopping time on its y axis. From here we can see that the points on the graph are not random at all; they have some kind of geometric pattern that is due to the 3x+1 in the odd case and x/2 in the even case. I have seen many attempts to...

From what I can tell off of Wikipedia and Wolfram, it doesn't look like this is currently known. Regrettably, I live in a social vacuum of mathematical pursuits, so I've come here in the hopes that someone can tell me if this is really new information or simply a retread. Brief Collatz...

Would it be possible to prove the collatz conjecture indirectly by demonstrating rules that apply to 'Collatz-like' conjectures? (I call anything where you simply change the values in the 3n+1 part of the conjecture to other values, holding everything else the same a Collatz-like conjecture)...

The conjecture states that: Given a positive integer n, If n is even then divide by 2. If n is odd then multiply by 3 and add 1 Conjecture: by repeating these operations you will eventually reach 1. Proof: Let n be the smallest positive integer that is a counterexample...

I have created a program in javascript that has tested integers on the collatz conjecture. Recall that the collatz conjecture says given any natural number n you must divide n by 2 if it is divisible by 2 and multiply n by 3 and add 1 if it is not divisible by 2. Repeat this process and you...

Hello there everyone! I've written a lovely little program to go through the tedious process of testing numbers in the "If odd 3n+1; If even n/2; Repeat." scenario. It then saves all of the numbers, starting with the integer being tested, and ending with "1" in a file of the form...

Hey, this is my first post, so... Hello everybody! I've been looking into the Collatz conjecture, and like most mathematically minded people, been completely absorbed by it. I'm looking to bounce some ideas off other people, kind of a peer review of a couple things if you will. I'll be the...

http://www-personal.ksu.edu/~kconrow/" I mean really read it, to where they understand it, not just to the point where their eyes glaze over? I see his site cited quite frequently, but I don't know if I've ever seen any critique. I admit, I was intimiitaded by his site at first. But...

The paper at this site "http://uts.awardspace.info" looked interesting to me, but would anyone else familiar with this problem, it's been around since the 30's, check it out and give an opinion.

LOGICAL SYSTEMS+NEW PRINCIPLES+ATTEMPT TO SOLVE COLLATZ CONJECTURE. First i would like to say that am honoured to share my thought with great people in here who always provide help.I will not say iam right or wrong.I hope this post will be aspark to good mindes. I have viewed the laws of...

LOGICAL SYSTEMS+NEW PRINCIPLES+ATTEMPT TO SOLVE COLLATZ CONJECTURE. First i would like to say that am honoured to share my thought with great people in here who always provide help.I will not say iam right or wrong.I hope this post will be aspark to good mindes. I have viewed the laws of...

Hey, i was reading about the Collatz conjecture, where, if you take a integer, divide it by 2 if its even and triple it then add one if it's odd, and do it over and over again, the result would be one. I was thinking, "wouldnt it have the same effect if you didnt triple odd numbers?" am i wrong?