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March 18th, 2017, 08:47 AM  #1 
Newbie Joined: Feb 2017 From: Bay Area, US Posts: 5 Thanks: 0 Math Focus: 3x+1  On the Collatz Conjecture
If you don't know what the Collatz Conjecture is, Wikipedia has a great description. I've noticed two things about numbers one less than a power of 2[1,3,7,15,31,...] The first is that (apart from 127)their height is equal to or less than the height of all previous numbers. I've checked up to (2^16)1, so it still may be incorrect. The second is that the (2n1)'th term of a number (2^n)1 will be 2f^n(2n1) where f(n)=(3n+1)/2. This term will be divisible by 4 as well, but not by 8. For this, I've checked up to (2^22)1 since after that Google Spreadsheets breaks. If anybody can prove these, it would be much appreciated. Thank you. 

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