Are there any functions with Big O (Busy Beaver(n))?

So, I was reading this article by Scott Aaronson on big numbers, and he mentioned that the Busy Beaver sequence increases faster than all sequences computable by Turing Machines. Faster than exponentials, faster than the Aaronson sequence, and faster than a recursive use of Knuth’s up-arrow notation.

This led me to a thought: are there any algorithms that grow in size with Big O (Busy Beaver(n)), aside from the Halting Problem? Is it even possible to design such an algorithm on that would run on a Turing Machine-equivalent computer?