A028434 Golc sequence in base 4. Left to right concatenation of n,int(log_4(n)),int(log_4(int(log_4(n)))),... in base 4.

4, 8, 12, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 264, 280, 296, 312, 328, 344, 360, 376, 392, 408, 424, 440, 456, 472, 488, 504, 520, 536, 552, 568, 584, 600, 616, 632, 648, 664, 680, 696, 712, 728, 744, 760, 776, 792, 808, 824, 840, 856, 872, 888