0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC

0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC (bbch) is the num(5) champion (the five-state, two-symbol TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho. It halts after 15590 steps with 165 consecutive ones on the tape.

It is tied for the num(5) championship with 1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB (bbch) which is the TNF-1RB version of the same TM (The permutation of this TM starting at state B).

Analysis

Let $A(a):=0^{\mathrm{\infty }}{1}^a\text{<mo><</mo>}\text{A}110^{\mathrm{\infty }}$. Then, $$\begin{array}{lll}A(3a)& \to & A(4a+2)\\ A(3a+1)& \to & A(4a+4)\\ A(3a+2)& \to & 0^{\mathrm{\infty }}\text{<mo><</mo>}\text{Z}{1}^{4a+5}{0}^{\mathrm{\infty }}\end{array}$$

Trajectory

This Turing machine starts with $A(3)$ after 13 steps and halts after 10 rule applications: $$A(3)\to A(6)\to A(10)\to A(16)\to A(24)\to A(34)\to A(48)\to A(66)\to A(90)\to A(122)\to 0^{\mathrm{\infty }}\text{<mo><</mo>}\text{Z}{1}^{165}{0}^{\mathrm{\infty }}$$