A102828 "True already", base 2, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 1.

1, 3, 7, 13, 19, 25, 31, 41, 47, 57, 65, 69, 75, 83, 91, 101, 109, 119, 131, 137, 143, 153, 161, 167, 177, 185, 195, 203, 213, 223, 237, 249, 261, 267, 275, 283, 293, 301, 311, 323, 331, 341, 351, 365, 377, 389, 397, 407, 419, 429, 441, 453, 463, 477, 491