The Collatz conjecture, the 3N+1 problem

Consider the following operation on an arbitrary positive integer:

If the number is even, divide it by two.
If the number is odd, triple it and add one.

It is named after Lothar Collatz, who first proposed it in 1937.
Also known as the Ulam Conjecture.
This is an example of a problem that is easy to state but very diffuclt to prove. It remains unsolved to this day

Category:

Science & Technology

Tags:

• Mathematics
• Tag
• system
• famous
• unsolved
• hard
• therom
• proof
• intergers

[BibleForDummies]

Should be 3n + 1 problem not 2n!

[MathDemos]

I'll change it right away thank you for pointing this out.

[Werelion2367]

@Mauromoustakos I'll try to add what is missing and put it in the subtitles and description once I reset the password to my MathDemos account.

[Mauromoustakos]

Two things are missing.

One is, that the question to prove is whether the sequence that is formed in the way you describe, always contains number 1, no matter which is the first term.

And the second missing thing is to tell us what is represented by the graph.

-.

[CHeCKEyE5]

I had an independent study on this problem in college. I ended up doing something similar by graphing all of the first iteration numbers, all of the second iteration numbers, and so on. I found, if i remember correctly, that every point fell on a perfect line with a patterned slope and y-intercept. I don't remember off the top of my head what the pattern was for either but it was pretty interesting in my opinion.

[jwm239]

...Ah! The "Collatz Comet"...two paths of broken lines - reminiscent of "Goldbach's Comet" when graphing that Conjecture.

[TheyCallMeConfucious]

i dont know what the problem is... :(

[MisterSir2]

...im not sure what im watching...

maybe an explanation is needed... :/