
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 18th, 2017, 09:47 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. 

Tags 
collatz, conjecture 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
collatz conjecture  isaac  Number Theory  6  March 15th, 2016 02:12 AM 
Collatz conjecture  isaac  Number Theory  37  April 3rd, 2015 03:54 AM 
About Collatz conjecture  vlagluz  Number Theory  10  November 5th, 2014 12:27 AM 
Collatz conjecture  jim198810  Number Theory  4  August 30th, 2014 08:17 AM 
Collatz conjecture & More (Please Help)  Aika  Number Theory  6  April 29th, 2012 07:34 AM 