3n+1. a.k.a. The Collatz Conjecture.

[science_man_88]

Originally Posted by mathwiz

Try to think of it this way:

Reasoning about different \(kn+c\) sequences is all well and good, and you can use a finite number of them to show the conjecture holds up to a certain \(n\) limit.

But if you want to use this approach to show the conjecture holds for all \(n\) then you'll need an infinite number of \(k\) and/or \(c\) to do it.

Okay sure. though for odd n

[LaurV]

Originally Posted by mart_r

and I might add the pertinent sequence A076227 here for further reading.

Thanks for sharing that. Getting those numbers is a 1-day work with a single core, silly pari script. Getting to 2^68 may be a week work (the time doubles with any bitlevel, similar to our TF bitlevels, because at every level b+1 you have to test all remaining classes x from the level b (mod 2^(b+1)), plus all classes x+2^b (mod (2^b+1)).

What is time-costly is to crunch all those remaining sequences, to see they terminate. Some of them are "millions", so the process will take time, even if you have a lot of computers, and even if each step is almost instant (division by 2 is cutting the last zero, in binary, and multiplication by 3 is just a shift and add).

My advice is, don't spend time with Colatz. Not only my advice, but from people who know what they say. Unless you are some genius mathematician, like Terrence Tao, or have that spark of genius like some of my colleagues had, you will only waste precious years of your life. It is catchy, because it looks so simple. Calculations like these, however, lead nowhere, unless you can find a counterexample (which is not probable, many mathematicians believe the conjecture is true).

[xilman]

Originally Posted by chalsall

Algebra is to Calculus as Chess is to Go.

Apples are to oranges as strawberries are to pineapples.

I will leave you to stew fruitfully for a while before explaining why.

[xilman]

Originally Posted by LaurV

My advice is, don't spend time with Colatz. Not only my advice, but from people who know what they say. Unless you are some genius mathematician, like Terrence Tao, or have that spark of genius like some of my colleagues had, you will only waste precious years of your life. It is catchy, because it looks so simple. Calculations like these, however, lead nowhere, unless you can find a counterexample (which is not probable, many mathematicians believe the conjecture is true).

+1

I spent a cpu year or so back in my naive youth.Likely a core-minute or few these days, thanks to Moore.

This one is only going to be solved by deep mathematics about which we barely have a clue right now.

A parellel might be FLT, which is also deceptively easy to state and yet remarkably difficult to prove.