Re: Collatz conjecture question

On Sun, 23 Mar 2025 11:19:03 +0100, efji <efji@efi.efji> wrote in
<vron6n$23ve9$1@dont-email.me>:

Le 23/03/2025 à 03:53, vallor a écrit :

The Collatz conjecture has come up in comp.lang.c, and it got me thinking
about it.
 
First, I'm not a mathematician, nor do I play one on TV.  But I wanted
to find out if there were any papers or other references that
have discussed the following:
 
To compute the next number in a series
Odd numbers: N = 3N+1
Even numbers: N = N/2
 
So it seems that for odd numbers, the next number in the series
will always be even; but for even numbers, the next number might
be odd or even.
 
And that's what I'm wondering about:  has anyone ever explored
whether or not the even operation would tend to "dominate" a
series, and that is why it eventually arrives at 1?

 
Nobody knows (yet) if it always arrives at 1...
The strongest result on the subject is due to Terence Tao
https://arxiv.org/abs/1909.03562
and it is quite away from the proof of the conjecture.
 
Numerically, a repartition of roughly 1/3 of odd numbers and 2/3 of even
numbers is observed, with a larger proportion of even numbers near
convergence. No proof at all for all this.
 
Good luck :)

Thank you for the reply, very much appreciated.

I also found this article:

https://www.researchgate.net/publication/361163961_Analyzing_the_Collatz_Conjecture_Using_the_Mathematical_Complete_Induction_Method

"Analyzing the Collatz Conjecture Using the Mathematical
Complete Induction Method"

--
-v