August 28th, 2014, 09:03 PM  #1 
Member Joined: Nov 2013 Posts: 62 Thanks: 0  Collatz conjecture
Missing anything?? Last edited by jim198810; August 28th, 2014 at 09:15 PM. 
August 29th, 2014, 06:05 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Of course $n_0$ does not have to be the base2 log as indicated. (Perhaps you meant the 2adic valuation, in which case that line is correct but the conclusion does not follow.)

August 30th, 2014, 04:49 AM  #3 
Member Joined: Nov 2013 Posts: 62 Thanks: 0 
by conclusion you mean 3xi+1<2^(log_2(cx0)) ? probably its not the right question to ask. if ni>1 then it should be quite easy to show. Question emerges when ni=1 for certain consecutive iteration.I might have a proof for that. 
August 30th, 2014, 07:16 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I mean the very first use of log, on the third line.

August 30th, 2014, 08:17 AM  #5 
Member Joined: Nov 2013 Posts: 62 Thanks: 0 
2^(log_2(3(x0)+1))=2^n1 * 2^(log_2(x1)) ? If I want to know the power of 2 on the right hand side , it must satisfy the left hand side. If I partition the left side in two part, in one part it is converted in power of 2,for other one, 2base logarithm has been used. 

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