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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

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

Posted: Jun 3, 2009 5:43 AM

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...

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