March 11th, 2016, 07:39 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, 05:37 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, 10:38 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, 01:09 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, 04:52 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, 01:03 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, 02:12 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 

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