March 11th, 2016, 06:39 AM  #1 
Member Joined: Jul 2014 From: israel Posts: 76 Thanks: 3  collatz conjecture
x = the numbers of even values in a cycle y = the numbers of odd values in a cycle 2^x3^y>0 x > y ln3/ln2 > y is there an upper limit to x in a way that i can write it with y somthing like: if ky > x then k=? can someone knows if and how i can find k? its seems that k can be above 2 or without limit ... 
March 12th, 2016, 04:37 AM  #2 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26 
Off the top of my head, I don't see how you could prove an upper limit without finding an upper limit on how long a cycle could be.

March 12th, 2016, 09:38 PM  #3 
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5 
You can get k in the Same way, you got the other direction of the inequality. Just notice 3n+1 < (3+1/n) n< (3+1/m) n wehre m is the spaltest number in the cycle. You can get a lower blind in m with the existing computational results. You wil get: Ln(3+1/m)/ln(2) y > x > ln 3/ln 2 y 
March 13th, 2016, 12:09 AM  #4  
Member Joined: Jul 2014 From: israel Posts: 76 Thanks: 3  Quote:
plus i want only y on the right side of the equation ... the whole point was to write the upper bound with only y  
March 13th, 2016, 03:52 AM  #5  
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5 
Sorry for the many typos. I have still to figure out how to switch between the auto corrects. But no need to get aggressive. Your Question was: Quote:
k=ln(3+ 1/m)/ln(2). Where m is a lower bound for the smallest element in your cycle. For instance if you accept that people have checked that no number below 1000 is in a cycle (except for 1,2,4) you could take m = 1000. Giving you a factor k only 1 in 3000 bigger than the lower bound you stated yourselve.  
March 14th, 2016, 12:03 AM  #6  
Member Joined: Jul 2014 From: israel Posts: 76 Thanks: 3  Quote:
but that is not what is asked i wanted an upper limit (without m) only written formula by y (for every y) x > y ln3/ln2 > y i wanna replace x with a formula that uses y only and not another factor  
March 15th, 2016, 01:12 AM  #7 
Member Joined: Jul 2014 From: israel Posts: 76 Thanks: 3 
nvm i found a way to do it problem solved you guys can close this thread 

Tags 
collatz, conjecture 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Collatz conjecture  isaac  Number Theory  37  April 3rd, 2015 02:54 AM 
About Collatz conjecture  vlagluz  Number Theory  10  November 4th, 2014 11:27 PM 
Collatz conjecture  jim198810  Number Theory  4  August 30th, 2014 07:17 AM 
Collatz conjecture & More (Please Help)  Aika  Number Theory  6  April 29th, 2012 06:34 AM 
Collatz conjecture, questions  xolruf  Number Theory  1  January 1st, 2012 08:11 AM 