Re: Collatz conjecture question

Le 23/03/2025 à 21:34, vallor a écrit :

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"
 

Wow, thanks for the link !
Obviously a false paper, written by non-mathematicians, and published in a predatory journal, making big money in publishing anything.
Of course they have not proven the Collatz conjecture using an hypothetic "Complete Induction Method" :)
It is a very strong conjecture, still unproven, and the link I have given is a recent paper from Terence Tao who is maybe of one the best mathematicians ever (including Euler, Gauss, Poincaré etc.).
--
F.J.