Numbers that converge on 85

This picture shows the tree containing all the numbers less than 1024 that converge on 85 = (256-1)/3. 633 is the furthest out, being 30 iterations from 1. Even numbers are omitted, being encapsulated in the small white boxes, for instance the '4' steps between 803 and 2141 includes 1606, 3212 and 6424.