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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 ]
 roupam.ghosh@gmail.com Posts: 96 Registered: 5/11/09
Re: Max. power of 2 and number of odd integers in a loop in the
Collatz problem

Posted: Jun 4, 2009 8:05 AM

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...

>
>

I have a proof for it... not my observation...

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