A102829 "True already", base 3, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 3 contains floor(a(n)/3) copies of the digit a(n) % 3, with a(0) = 1.

1, 2, 4, 5, 8, 13, 14, 17, 23, 29, 32, 35, 41, 44, 50, 56, 62, 67, 74, 76, 82, 88, 92, 95, 98, 104, 110, 113, 116, 122, 125, 131, 137, 143, 152, 161, 173, 179, 188, 193, 202, 206, 215, 223, 226, 232, 238, 244, 250, 256, 263, 269, 274, 278, 284, 287, 293, 299