5-state busy beaver winner

The 5-state busy beaver champion (and winner!) is: 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch). It was found by Heiner Marxen and Jürgen Buntrock in 1989. The machine halts after 47,176,870 steps and with 4098 1's on the tape, showing that $BB(5)\geq 47{,}176{,}870$ and $\Sigma (5)\geq 4098$.

Behavior

This machine repeatedly applies the following map, starting with $x=0$:

$${\begin{aligned}g(x)&\to {\frac {5x+18}{3}}&&{\text{if }}x\equiv 0{\pmod {3}}\\g(x)&\to {\frac {5x+22}{3}}&&{\text{if }}x\equiv 1{\pmod {3}}\\g(x)&\to {\text{HALT}}&&{\text{if }}x\equiv 2{\pmod {3}}\end{aligned}}$$

which can alternatively be written as:

$${\begin{aligned}g(3k)&\to 5k+6\\g(3k+1)&\to 5k+9\\g(3k+2)&\to {\text{HALT}}\\\end{aligned}}$$

The full orbit from $x=0$ is:

$${\begin{array}{l}0&\to &6&\to &16&\to &34&\to &64&\to &\\114&\to &196&\to &334&\to &564&\to &946&\to &\\1584&\to &2646&\to &4416&\to &7366&\to &12284&\to &{\text{HALT}}\end{array}}$$