A028889 Numbers n such that iterated product of digits of n is a power of 2.

1, 2, 4, 8, 11, 12, 14, 18, 21, 22, 24, 26, 27, 29, 34, 36, 37, 38, 39, 41, 42, 43, 46, 49, 62, 63, 64, 66, 67, 72, 73, 76, 77, 79, 81, 83, 88, 89, 92, 93, 94, 97, 98, 99, 111, 112, 114, 118, 121, 122, 124, 126, 127, 129, 134, 136, 137, 138, 139, 141, 142, 143, 146, 149, 162, 163, 164, 166, 167