Problem Statement

The Kolakoski sequence is an infinite sequence of natural numbers, (excluding zero); with the property that: This is not a Kolakoski sequence: Its sequence of run counts, (sometimes called a run length encoding, (RLE); but a true RLE also gives the character that each run encodes), is calculated like this: The above gives the RLE of: The original sequence is different from its RLE in this case. It would be the same for a true Kolakoski sequence. Lets start with the two numbers (1, 2) that we will cycle through; i.e. they will be used in this order: 1,2,1,2,1,2,.... We will arrange that the k'th item of s states how many times the last item of sshould appear at the end of s. We started s with 1 and therefore s[k] states that it should appear only the 1 time. ... Note that the RLE of 1, 2, 2, 1, 1, ... begins 1, 2, 2 which is the beginning of the original sequence. The generation algorithm ensures that this will always be the case. (There are rules on generating Kolakoski sequences from this method that are broken by the last example)

Let's start with the solution: