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.
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