h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: The 3n+1 Problem (A Probabilistic Approach) - A87739212
Author: smallfrey - U13668064

As the "bug" wearing the Edgar suit said, "Here. Is this any better?".

I still have to read the whole Entry. Could you maybe write a short introduction to this at the beginning? Something like where this problem you talk about occurs? And for which calculations it is needed to know about this?

Hmmm... I would probably do the whole thing differently. First say what a step in your calculation is about, then write down the foruma (is it called like that in English?) and then explain every 'letter' in the formula if it hasn't been done already in an earlier step and give additional explainations.

Does that help?

There's already an entry in the Guide (you can find it doing a Browse) that gives an introduction to the problem and some of the history of its origin. I was exploring the possibility of the article I just submitted as being some kind of "add-on" to that entry (to avoid duplicated entries). My article would be somewhat more involved than the original article (maybe too involved to be of much general interest). I suppose one could identify each individual symbol in a formula and discuss it, although it would turn out to be a verbose article. Maybe your suggestion does help; we'll see what the other reviewers say. Thanks.

Then maybe you can link to it: A565788

Could you maybe add a first sentence linking to that other Entry and telling that people should read it before reading yours?

Yes, I'm waiting to see what Gnomon thinks.

Today's 02-17-12 and I discovered that the number of prime factors of 2^(K+L)-3^K can be modeled using a Poisson probability distribution.

I think the mathematics in this is way beyond the average reader. I couldn't make much of it, and I don't want to spend a huge amount of time wading through it. If you stated what the purpose of the Entry is, and what your conclusions are, it might make it worth reading.

Have you discovered something new? Does the information presented prove the conjecture for some value of d other than 1? Does it help build up a picture of the sequence general behaviour? Is there any reason to believe this will help with the case of d=1?

Thanks for replying. The purpose of the entry is to investigate another way to tackle the 3n+1 problem and the conclusion is pretty much that a Poisson probability distribution can be used to model the number of cycles. Much of the article suggests a way to explain the origin of this probability distribution. It's quite all right with me that it's not going to be an Edited Guide Entry (I appreciate your input regardless). I use h2g2 as a place where other people can come to read the article and the conversations are useful to me as a way of documenting my discoveries (obviously, I think the article is worth something). One world-class expert in the field read the article, asked for some clarification, and suggested that my Proposition (1) might need to be amended so that d was prime (I couldn't find any evidence of this). He also liked my website. I also submitted a link to Reddit math (in your neck of the woods) and got 12 likes and 4 dislikes. As far as I can tell, this is new (but I haven't done an exhaustive search of the literature). This approach doesn't prove anything for any d value. That's the point; it appears to be random and unprovable.

I think that formatting it better would benefit the mathematicians reading it as well as the amateurs like myself. Stating your purpose and conclusions clearly at the start will benefit everyone.

I added an abstract at the beginning of the article. Hopefully, this gives a good introduction. It occurred to me today that two independent Poisson variables are at play here. So now I have a preliminary explanation of the cycle counts. Much work remains to be done though.