Hi. This small corner of the Internet contains my share of knowledge on (mostly) computer science and software development explorations that I’ve recently started to sporadically document after over 25 years of silent accumulation.
Hopefully the information here will assist someone in some way.
If you have comments, questions or just a cool idea that might be worth pursuing, send an email to amnon [dot] david [at] gmail [dot] com
I have published a proof of the convergence of Collatz conjecture that might interest you. Here is the link: https://doi.org/10.1155/2019/6814378
abstract:
A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by that follows a recurrent pattern of the form , where represents divisions by 2 more than once. The sequence presents a probability of 50:50 of division by 2 more than once as opposed to division by 2 once over the even natural numbers. The sequence also gives the same 50:50 probability of consecutive Collatz even elements when counted for division by 2 more than once as opposed to division by 2 once and a ratio of 3:1. Considering Collatz function producing random numbers and over sufficient number of iterations, this probability distribution produces numbers in descending order that lead to the convergence of the Collatz function to 1, assuming that the only cycle of the function is 1-4-2-1.
Very interesting. Thank you for bringing this to my attention.
You wrote:
“Considering Collatz function producing random numbers and over sufficient number of iterations,.”…
In my post about this (http://nocurve.com/virtual-lab/contemplating-the-collatz-conjecture-3n1/) , I mentioned that as far as I can tell, this is the problematic part of the proof is that while it appears to be the case that the Collatz function produces random numbers, this is exactly what needs to be proved to employ the probabilistic proof.