20180727, 21:03  #1 
"David Barina"
Jul 2016
Brno
2^{3}·5 Posts 
A new problem similar to the Collatz problem
I am concerned with the 7x±1 problem. My conjecture is that the orbit of arbitrary positive integer always leads to 1. I have computationally verified the conjecture for all numbers up to 10^{10}. I would appreciate hearing any thoughts on this. Thanks!

20180728, 14:03  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:
got buried within the underline on my terminal. Its display is a bit fuzzy. 7x+/1 should converge because when we select +1 or 1 depending on 7x mod 4 we pick up an extra factor of 2. (7/8)^n as opposed to (7/4)^n behaves very differently. I apologize profusely. It is clear, however, that the pure 7x+1 iterations do NOT converge. 

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