Re: Collatz conjecture question

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 :)
--
F.J.