A018136 Powers of fifth root of 8 rounded to nearest integer.

1, 2, 2, 3, 5, 8, 12, 18, 28, 42, 64, 97, 147, 223, 338, 512, 776, 1176, 1783, 2702, 4096, 6208, 9410, 14263, 21619, 32768, 49667, 75281, 114105, 172951, 262144, 397336, 602249, 912838, 1383604, 2097152