Isn’t it a true coincidence? Collatz-like problems are one of the simplest (in operation), no surprise that BB(low n) chooses them. It’s probably more surprising that we found it before analyzing BBs.

I wonder if this is something generally true for all BB's and if Collatz-like functions represent some kind of of limit of decidability.

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Is there a more "popular science" description of what is being said here. I would like to understand what is meant by "Collatz-like". Is it a function like:

  f(n) = {n/2 : for even n,
          3n+1 : for odd n}  

What does

  M(n) = 0^inf < A 1^n 0^inf.

I have really enjoyed the Busy Beaver stuff and play with simple code to try and learn what I can but when I read about it I run into the brick wall of math reading comprehension. Numberphile on youtube is pretty good sometimes with explanations but is not a reference. I do not know where to turn (I might ask chatGPT just to see what happens).

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