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From: efji <efji@efi.efji>
Newsgroups: sci.math
Subject: Re: Collatz conjecture question
Date: Sun, 23 Mar 2025 21:59:08 +0100
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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.