A Sequence That Describes Itself

Consider the infinite sequence of digits 1 and 2 that begins like this: 1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 … Split it into runs of equal adjacent digits: 1 | 22 | 11 | 2 | 1 | 22 | 1 | 22 | 11 | …. Writing down the run lengths in order gives 1 2 2 1 1 2 1 2 2 …, which is the sequence itself. The runs alternate between ones and twos. The opening 1 2 2 together with this rule determines the whole sequence. Given length, count the ones among the first length digits of the sequence.

length=9 → 4

length=3 → 1

length=20 → 10