Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Max. power of 2 and number of odd integers in a loop in the Collatz
problem

Replies: 7   Last Post: Jun 6, 2009 4:45 PM

 Messages: [ Previous | Next ]
 mensanator Posts: 5,039 Registered: 12/6/04
Re: Max. power of 2 and number of odd integers in a loop in the
Collatz problem

Posted: Jun 4, 2009 1:11 PM

On Jun 4, 7:05 am, roupam <roupam.gh...@gmail.com> wrote:
> On Jun 3, 10:41 pm, Mensanator <mensana...@aol.com> wrote:
>
>
>
>
>

> > On Jun 3, 4:43 am, roupam <roupam.gh...@gmail.com> wrote:
>
> > > I have found, that if there exists a loop, then if
> > > n = number of odd integers in the loop
> > > k = maximum power of 2 that divides a number in the loop
> > > then, the following conclusions hold...
> > > for positive integers
> > >    k <= n+1
> > > for negative integers
> > >    k < n log3//log2 - n + 1
> > > Consider the negative loop starting with
> > > -17 -50 -25 -74 -37 -110 -55 -164 -82 -41 -122 -61 -182 -91 -272 -136
> > > -68 -34 and then back to -17
> > > Here...
> > > n = 7
> > > k = 4
> > > 4 < 7 * log3/log2 -7 + 1 = 5.09...

>
> > What does this follow from, other than your observation?
>
> I have a proof for it... not my observation...

The 2nd greatest fallacy is the notion that evidence
constitutes proof.

The greatest being the notion that testimony constitutes
evidence.

Date Subject Author
6/3/09 roupam.ghosh@gmail.com
6/3/09 mensanator
6/3/09 Guest
6/4/09 roupam.ghosh@gmail.com
6/6/09 Tim Smith
6/4/09 roupam.ghosh@gmail.com
6/4/09 mensanator
6/6/09 mensanator