What is the method behind the 3x+1 problem?

[Trurl]

3x+1 if odd

x/2 if even

 

 

So why not create a sieve of multiples of 2, 4, and 8?

 

When x equals a logarithm of 2, 4, or 8 then x/2 repeated equals 2.

 

2*2*2*2…

 

4*4*4*4…

 

8*8*8*8…

 

These 3 logarithms of 2, 4, and 8 encompass all the numbers that reduce to 2 when repeatedly divided by 2.

 

What am I missing? Did I break the rules of the pattern? I am trying real hard not to factor semiPrimes. I did not research the problem yet. I am only working with 3x+1.

 

I realize that this is more complex with larger numbers. I am just stating a simple example.

[MigL]

Here is a ( long ) video illustrating some of the approaches to understand the Collatz Conjecture

 

[KJW]

The Proof of the 3X + 1 Conjecture

 

 

Edited January 15 by KJW

[MigL]

I don't really understand the proof, but I find some of the approaches interesting.

Edited January 15 by MigL