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Kolakoski sequence

Synonym: 
Kolakowski's sequence
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

11Y55 no label found94A55 no label found

Comments

Simple question. (Perhaps too dumb.) Is there any difference if we change in Kolakoski sequence 2's with zeroes (0)? I guess there are no differences in densities of 1 and 2 (0). They would probably be in terms as sums and such are.

Is a term strongly recurrent sequence already defined somewhere within PlanetMath. If not, it would be fine to explain it a bit.

Well, I can replace the 2's by 0's, of course, but then the sequence stops being "self describing": 1,0,0,1,1,0,0,... doesn't consist of one 1, then zero 0's, then 0 1's, then one 0, then...

But 1,2,2,1,1,2,2,... *does* consist of one 1, then two 2's, then two 1's, then ...

Regarding "strongly recurrent sequence": no, it's defined nowhere. I've already requested "topological dynamics" and "symbolic dynamics", which are the right contexts in which to develop "recurrent sequence" and "strongly recurrent sequence". Sorry.

[ariels] thank you for reply. I like very much talking "(almost) ALIVE" about math and even about its the most difficult fields. As a sentence says: Math for the people, by the people... Interesting subject - no doubt. I admit I have to study some more to fully understand this kind of integer sequences. I guess I had missed a term "self describing". Nice. Another "stupid" question. Is such new sequence 1, 0, 0, 1, 1, 0, 0, ... really new or how should I better ask? Yes, there's no doubt this is "some kind" of sequence but, hey... I'll try to define it somehow. Or perhaps this has already been done.

"Recurrent sequence" also sounds very interesting. Best regard.

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