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December 31st, 2011, 11:48 PM  #1  
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  Collatz conjecture, questions
This is probably wrong, but here goes. (http://en.wikipedia.org/wiki/Collatz_conjecture) Since the conjecture has been verified upto a certain limit, proof by contradiction? Let C be the smallest number to contradict the Collatz conjecture. C1 would mean the next term in the Collatz sequence, C2, and so on. If C is even, C=2N. C1=N. As C is the smallest contradiction to the conjecture, C1 has a sequence to 1. Therefore C must be odd. Let C=2N+1 Quote:
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[/quote:35ksggzg] After any substitution, we get the case C= (Multiple of 2^x)+(2^x1) and can't simplify without another substition. (They are in bold) If it is shown above cases always have a sequence, would it be a proof? Also please share your attempts at this fun 'little' problem! PS: Still learning LaTeX  
January 1st, 2012, 09:11 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  Re: Collatz conjecture, questions
You can always find residues that work mod 2^n for any n. The number of residues increase at some pointI'm not sure if your calculations are right up to this point or not (I checked only about half, which looked good) but it does go to 

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