Help me identify maths problem

[Solver]

There's a problem in maths, IIRC, yet unsolved, but I don't remember the name. Tried Googling, but to no luck.

Here's the essence of it.

Take any number. If the number is odd, multiply it by three and add 1. If not odd, divide by 2. Do the same with the result. In the end, you'll always come to 4,2,1, which repeat forever. Like:

40. Not odd, divide by 2 =20. 20:2=10. 10:2=5. 5 odd, 5*3+1=16. 16:2=8 8:2=4 4:2=2 2:2=1 1*3+1=4

Obviously, 4,2,1 will repeat itself.

There were some good docs on this problem online, but please someone help me get the name of it!

[Eli]

It starts with M. I had to write a program that does stuff with this series once and I remember that I used M as the array name.

[Japher]

What a silly observation, IMO.

[Ramo]

Is the word you're looking for "recursive?"

And what's unsolvable about it? Looks pretty straightforward.

1. If you have an odd number you can represent it as, where z is an integer, 2z + 1. So if you multiply by 3 and add one, you have 6z + 4, which is even and proceed to step two.
2. If you have an even number, you can represent it as 2z. So if you halve it, you have z. If z is even, you repeat step two. If it's odd, you can generate another even number by step one. Through this process, you'll eventually generate a number that's 2^z*, where z* is a positive integer, which this algorithm reduces to 2², 2¹, 2⁰.

[Eli]

Nope, not M.

Collatz is the name.

[Solver]

Wrote a program too, to check some things with it .

Ramo - it's unsolved, as it hasn't been proven. It goes down to 4,2,1 each time, but that hasn't been proven yet. While it seems simple, there's some very complex conjenctures and stuff involved...

[Solver]

Collatz Problem it is, thanks!

Anyone interested take a look here http://www.cecm.sfu.ca/organics/pape...tml/node2.html , some pretty darn complex stuff surfacing!

[Guest]

Ramo
how do you know you'll eventually reach a power of 2?
thats the key hole in you reasoning.
I seem to have read about this a year or so ago. Not sure its this exact one but sounded something like it and the exact proof was still not done at the time.

[Ramo]

Yep, couldn't find an answer to that.

[MrFun]

I hate math . . . . .

[Urban Ranger]

That's called the Syracause Algorithm.

[Panag]

hi ,

, Solver why dont you ask one of them internet math solution site's , ......


have a nice day

[Solver]

Panag, it's an *unsolved* problem.

[DAVOUT]

If in the algorythm, instead of multiplying the odd numbers by 3 and add 1, we just add 1, the sequence repeting itself becomes 2,1. It looks like the multiplication by 3 was just there to make the repeting sequence 4,2,1.

But what was the question ?

[Solver]

Multiplication by 3 is to get you a bigger even number then...

Question is... prove it! Noone has.