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I linked to a blog post about Collatz-like problems https://news.ycombinator.com/item?id=41609578

But before that and after I tried to link to another by the same author, which I thought is even more interesting, but for some reason didn't get any attention :(

https://news.ycombinator.com/item?id=41637592

It's about the "first"/"smallest" program (in terms of the number of turing machine states needed to describe it - 6), that humanity doesn't know how to solve.

A codegolfed Python program with its behavior (by mxdys):

    a,b=8,3
    while b:a+=a>>1;b+=2-a%2*3

Does this halt or not?

Knowing this will be necessary to prove the value of the 6th busy beaver number (the 5th has been recently proven).