A102830 "True already", base 4, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 4 contains floor(a(n)/4) copies of the digit a(n) % 4, with a(0) = 1.

1, 2, 3, 5, 6, 7, 10, 11, 15, 21, 22, 23, 26, 27, 31, 38, 39, 43, 47, 55, 62, 66, 70, 71, 74, 75, 79, 86, 87, 90, 91, 95, 102, 103, 107, 111, 119, 126, 130, 135, 139, 143, 151, 155, 159, 167, 171, 175, 183, 191, 203, 210, 214, 218, 223, 226, 234, 237, 241, 245, 250