User blog comment:Wythagoras/Step for step HAN and Dollar Function FGH analysis/@comment-5529393-20131030130205

According to your rule 12,

a$[0, 1]2 = a$ [...[[0, 0]2, 0]2 ..., 0]2 = a$[...[[0]2 ]2 ... ]2 = a$ [0]3 ~ phi(2,0), not

$[0, 1]2 = a$ [...[[0, 1], 1]..., 1].