A036463 Conjecturally, a power of 2 written in base 3 cannot have this many 2's.

42, 281, 375, 416, 593, 736, 907, 975, 1096, 1193, 1298, 1330, 1401, 1420, 1463, 1577, 1633, 1707, 2281, 2288, 2460, 2712, 2759, 3085, 3135, 3412, 3599, 3722, 3823, 4328, 4337, 4365, 4546, 4711, 5116, 5215, 5243, 5291, 5299, 5415, 5436, 5449, 5710, 5726