A102826 "True already", base 4, start 0: 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) = 0.

0, 1, 2, 3, 4, 6, 7, 8, 11, 12, 16, 18, 19, 22, 23, 26, 27, 31, 32, 39, 40, 43, 44, 48, 55, 56, 60, 64, 69, 70, 74, 75, 79, 86, 87, 90, 91, 95, 96, 103, 104, 107, 108, 112, 119, 120, 124, 128, 138, 139, 143, 151, 152, 155, 156, 160, 163, 167, 171, 172, 176