Yeah, Collatz operation is: if it's even divide by 2, otherwise multiply by 3 and add 1.
The gp post is asking: what if you make a procedure that runs that on a given input number, repeatedly, until you end up with the output 1, and give the sequence of numbers you visited on the way. Is that an algorithm?
Every number we've tried so far does go to 1, but it's unproven if they all do. It's possible that there exist cycles not containing 1, or maybe some inputs go to infinity. We haven't been able to prove either way.
> [...] the definition he used was that an algorithm must be executable on a Turing machine
Yeah, that's a pretty good reason to choose a certain definition of an algorithm (that otherwise might be awkward) when you have a model you're fitting it into.
The gp post is asking: what if you make a procedure that runs that on a given input number, repeatedly, until you end up with the output 1, and give the sequence of numbers you visited on the way. Is that an algorithm?
Every number we've tried so far does go to 1, but it's unproven if they all do. It's possible that there exist cycles not containing 1, or maybe some inputs go to infinity. We haven't been able to prove either way.
> [...] the definition he used was that an algorithm must be executable on a Turing machine
Yeah, that's a pretty good reason to choose a certain definition of an algorithm (that otherwise might be awkward) when you have a model you're fitting it into.