Google search says GSeq is computable, which makes sense since there's a recipe to follow for computing it. However, the calc of how long process takes to terminate is not

From Google AI search result:

Yes, the Goodstein sequence is computable, but the function that maps a starting number to the number of steps it takes for the sequence to reach zero is not provably total in Peano Arithmetic (PA). While a Turing machine can enumerate the sequence and determine when it reaches zero, the proof of termination relies on principles beyond PA