Problems in number theory from busy beaver competition

Understand

By introducing the busy beaver competition of Turing machines, in 1962, Rado defined noncomputable functions on positive integers.

• The study of these functions and variants leads to many mathematical challenges.
• This article takes up the following one: How can a small Turing machine manage to produce very big numbers? It provides the following answer: mostly by simulating Collatz-like functions, that are generalizations of the famous 3x+1 function.
• These functions, like the 3x+1 function, lead to new unsolved problems in number theory.