NJAS: "Once some of the sequences have been created, can someone post the A-numbers here?" I just noticed A359207 [number of steps to reach 0 starting with n in the map x->A359194(x) (binary complement of 3n), or -1 if 0 is never reached]. So, A359208 (maximum value reached) and A359209 (starts that never exceed the start) are also referenced.