Scratch

That's neat. 

Are you sure this is a real, unproved conjecture?  It's a fairly easy proof.

You see, as soon as you get to a number 2^n, which is the following pattern:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...

You automatically go straight down to 1, because every time you divide by 2 you get another even number, until 1.  Plus, every time you take an odd number, multiply by 3 and add 1, you get an even number.  So you will always get an even number 2^n eventually, which will bring you down to 1.

A project I made has so far proved this beyond 1000.

Last edited by Greenatic (2011-09-21 17:27:04)

cpumaster930 wrote:

Greenatic wrote:

Are you sure this is a real, unproved conjecture?  It's a fairly easy proof.

You see, as soon as you get to a number 2^n, which is the following pattern:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...

You automatically go straight down to 1, because every time you divide by 2 you get another even number, until 1.  Plus, every time you take an odd number, multiply by 3 and add 1, you get an even number.  So you will always get an even number 2^n eventually, which will bring you down to 1.

A project I made has so far proved this beyond 1000.

Someone already proved it for all numbers up to around 5.48 x 10^18. Have fun with your project xD

Anyway, you'd have to prove somehow that eventually, you'll reach a power of 2, in order to prove it your way. 

Well, a power of 2 is the only way to get to 1.  So, borrowing their proof...done.  And I thought you said this was unsolved?

I just made this based on the Collatz Conjecture:  http://scratch.mit.edu/projects/Greenatic/2040732  Might be interesting to some of the posters on this thread.

4lover wrote:

Greenatic wrote:

cpumaster930 wrote:

Someone already proved it for all numbers up to around 5.48 x 10^18. Have fun with your project xD

Anyway, you'd have to prove somehow that eventually, you'll reach a power of 2, in order to prove it your way. 

Well, a power of 2 is the only way to get to 1.  So, borrowing their proof...done.  And I thought you said this was unsolved?

But how do they know if all numbers will ever get to a number 2^n?

Here is where I reference Occam's Razor: http://en.wikipedia.org/wiki/Occam's_razor

Basically:

Wikipedia wrote:

Occam's razor (or Ockham's razor) often expressed in Latin as the lex parsimoniae, translating to law of parsimony, law of economy or law of succinctness, is a principle that generally recommends, when faced with competing hypotheses that are equal in other respects, selecting the one that makes the fewest new assumptions.

(emphasis by me)

Therefore, we need not make the assumption that something will change after 5.48 x 10^18, and we can assume that it will continue.  In other words, conjecture proven.

Occam's Razor is basically a slap in the face to complicated mathematics.   

Last edited by Greenatic (2011-09-21 20:22:29)