0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC

0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC (bbch) is the num(5) champion (the BB(5) TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho. It halts after 15590 steps with tape

$$0^{\mathrm{\infty }}\text{<mrow data-mjx-texclass="ORD"><mo><</mo>Z</mrow>}{1}^{165}{0}^{\mathrm{\infty }}$$

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 by Shawn Ligocki

A(a, b) = $ 1^a <A 11^b $

A(a+3, b) -> A(a, b+2)
A(0, b) -> A(2b, 1)
A(1, b) -> A(0, b+1)
A(2, b) -> $ <Z 1^{2b+3} $

A(3k,   1) -> A(4k+2, 1)
A(3k+1, 1) -> A(4k+4, 1)
A(3k+2, 1) -> $ <Z 1^{4k+5} $

@13: A(3, 1)

Trajectory of "a" values starting from A(3, 1):
3 6 10 16 24 34 48 66 90 122 Halt(165)