I came across the Placid Platypus function $PP(n)$ today, defined as the minimal number of states needed for a turing machine that prints a string of $n$ ones and halts. This function is claimed to (eventually) grow faster than any computable function, similar to the busy beaver function.
However, it is trivial to upper bound this function: consider the turing machine with $n+1$ states. It's transition function is simply (have it start in state 1):
- If in state $k \leq n$, go to state $k+1$, write $1$ on the tape, then move left
- If in state $n+1$, halt
This will write a string of $n$ ones, thus, $PP(n) \leq n+1$, disproving the claim that the Placid Platypus function grows faster than any computable function.
What am I missing?