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Old 2018-07-27, 21:03   #1
dabler
 
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"David Barina"
Jul 2016
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Default 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 1010. I would appreciate hearing any thoughts on this. Thanks!
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Old 2018-07-28, 14:03   #2
R.D. Silverman
 
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Quote:
Originally Posted by dabler View Post
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 1010. I would appreciate hearing any thoughts on this. Thanks!
I hereby eat some crow. I read the problem as 7x+1, not 7x+/-1 . The minus sign
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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