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The Busy Beaver function is a function that takes n as a number of states and returns the maximum finite number of ones that a 2-symbol turing machine with that number of states could produce. This pdf (https://www.scottaaronson.com/papers/bb.pdf) is the current (as of 2020) state of knowledge on this function. update from 2022: https://scottaaronson.blog/?p=6673