The busy beaver function Σ(n) is not computable, at least, not for every n. If it were, it could be used to determine if an arbitrary Turing machine halts, solving the halting problem.
To get from this non-computable function to a non-computable number, you can construct the finite number R = 0.Σ(1)Σ(2)Σ(3)... that concatenates all busy beaver numbers. Its first few digits are R = 0.1621 ... (thanks to ChatGPT for this step).
The busy beaver function Σ(n) is not computable, at least, not for every n. If it were, it could be used to determine if an arbitrary Turing machine halts, solving the halting problem.
To get from this non-computable function to a non-computable number, you can construct the finite number R = 0.Σ(1)Σ(2)Σ(3)... that concatenates all busy beaver numbers. Its first few digits are R = 0.1621 ... (thanks to ChatGPT for this step).