User:Wythagoras/Rado's sigma function/BB(4,5)

\(\Sigma(4,5)> 2^{\Sigma(2,5)}\)

0 _ 1 l 1 0 1 2 r 0 0 2 1 l 0 0 3 2 r 1 0 4 2 r 0 1 _ _ l 0 1 1 2 r 1 1 2 3 r 1 1 3 4 r 0 1 4 1 l 3 2 _ 1 r 2 2 1 _ l 2 2 2 1 r 3 3 1 1 l 3 3 2 2 l 3 3 _ _ r 2 3 3 2 r halt 3 4 3 l 3

Explanation
The first part is the machine for \(\Sigma(2,5)\). It outputs: 222...22241 (~1.7*10^352 2's)         ^ Then state 3 brings the head to the beginning of the string of two's, and changes two of them to ones. Then for each 2 the number of ones will be duplicated. It uses LittlePeng9's duplication machine.