alt Hacker NewsCan't you trivially force this to happen for any sequence?
1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 4, 4,
Goes to
1, 3, 3, 3, 2... Etc.
I could extend this trivially too since the bottom sequence trails the sequence we write up top. If i wanted another '2' down the bottom whatever number i choose up top i just write twice right?
So there's nothing about this particular sequence? I can just create any such sequences trivially; Whenever you start a new count, choose a random number and repeat for a many times as needed for the trailing sequence to match the top sequence.
It seems that this particular variant is uninteresting in the broader picture right? I could write another similar one
2, 2, 1, 1, 2, 1
2, 2, 1, 1, ... etc.
I don't get the specialness here?
>Can't you trivially force this to happen for any sequence?
No, because there's no deterministic way to infinitely extend that sequence. In your first example:
What are the values of x and y?>Whenever you start a new count, choose a random number and repeat for a many times as needed for the trailing sequence to match the top sequence.
You answered your own question. The Kolakoski sequence is special because it does not just pick a random number: the sequence is deterministically encoded by the run lengths, and vice versa.