User:Wythagoras/Rado's sigma function/BB(7,5)

\(\Sigma(7,5) > 2 \uparrow^{3}(1.7 \cdot 10^{352})\) 0 _ 1 r 1 0 1 2 l 0 0 2 1 r 0 0 3 2 l 1 0 4 2 l 0 1 _ _ l 0 1 1 2 r 1 1 2 3 r 1 1 3 4 r 0 1 4 2 l 6 2 _ 1 r 2 2 1 _ l 2 2 3 1 l 3 2 4 3 l 4 2 2 4 r 5 3 1 1 l 3 3 _ 1 r 2 4 1 3 l 4 4 _ 1 r 2 5 _ _ r halt 5 2 2 l 6 6 4 4 l 6 6 2 2 l 6 6 1 4 l 6 6 _ 1 r 2

Explanation
The first part is the machine for \(\Sigma(2,5)\). It outputs: 222...22241 (~1.7*10^352 2's)         ^

Then state 6 brings the head to the beginning of the string of two's, and adds a one. Each 3 duplicates the number of ones. For each 4 all the 1s will be changed into 3s, giving a function comparable to \(2^n\). For each 2 all the 3s will be changed into fours, giving a function comparable to \(2\uparrow\uparrow n\). It uses LittlePeng9's duplication machine.