Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.