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 $BB(5)\ge 47,176,870$ and $\mathrm{\Sigma }(5)\ge 4098$.

Behavior

This machine repeatedly applies the following map, starting with $x=0$: $$\begin{array}{rlrl}g(x)& \to \frac{5x+18}{3}& & \text{if }x\equiv 0(\mathrm{mod}3)\\ g(x)& \to \frac{5x+22}{3}& & \text{if }x\equiv 1(\mathrm{mod}3)\\ g(x)& \to \text{HALT}& & \text{if }x\equiv 2(\mathrm{mod}3)\end{array}$$which can alternatively be written as:

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

The full orbit from $x=0$ is: $$\begin{array}{lllllllllll}0& \to & 6& \to & 16& \to & 34& \to & 64& \to & \\ 114& \to & 196& \to & 334& \to & 564& \to & 946& \to & \\ 1584& \to & 2646& \to & 4416& \to & 7366& \to & 12284& \to & \text{HALT}\end{array}$$