Can You Prove the Collatz Sequence

(and become the next mathematics rock star!)

 

A Collatz Sequence starts with an integer i that is greater than one.

 

        

Normal Form

      

Short Form

 If i is even:
 If i is odd:

  

then i=i/2.

then i=3i+1.

  

then i=i/2.

then i=(3i+1)/2.

 

It has been shown, but never proven, that all such sequences will end in one.

See for yourself.

Enter any integer greater than one, and a Collatz Sequence will be generated.

If you wish to see the short form of the sequence, check the box.

In the center a graph of the sequence is displayed.

On the right the binary representation of the sequence is displayed

How does the length of the sequence change with i?

 

Starting Integer:

 

Short Form:                   

 

 

Graph of the Sequence

Decimal-Binary-Base 3 Sequence