(* _Michael De Vlieger_, April 19, 2024 *)
(* memoizes A060445 and samples as necessary to generate A177789   *)
(* otherwise, functions essentially the same as Tony Noe's program *)
c = 1 + Log2[3];                     (* constant                   *)
nn = 14;                             (* rows to generate, minus 1  *)
(* generate dropping times for odd numbers less than a threshold   *)
s = {1}~Join~Table[-1 + Length@ 
 NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, k, # >= k &], 
 {k, 2 Range[Floor[#/2] - 1] + 1}] &[2^Floor[Log2[3^(nn - 1)] + 1]];
                                                      (* ^ A060445 *)
{{0}, {1}}~Join~Reap[
Do[m = 2^Floor[Log2[3^(n - 1)] + 1];                  (* 2^A020914 *)
   t = Floor[1 + c (n - 1)];                          (* A122437   *)
   Sow[2 Position[s[[;; Floor[m/2] - 1]], t][[All, 1]] - 1], 
 {n, 3, nn}] ][[-1, 1]] // Flatten