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A306366
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For any sequence s of positive integers without infinitely many consecutive equal terms, let T(s) be the sequence obtained by replacing each run, say of k consecutive t's, with a run of t consecutive k's; this sequence corresponds to T(K) (where K denotes the Kolakoski sequence A000002).
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2
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1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1
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OFFSET
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1,2
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COMMENTS
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If s is finite, then s and T(s) have the same sum.
When s has no consecutive equal terms, then T(s) is all 1's (A000012).
Apparently, T^4(K) = T^2(K) (where T^i denotes the i-th iterate of K).
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LINKS
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FORMULA
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EXAMPLE
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The first terms of the Kolakoski sequence are:
+-----+ +--+ +-----+ +-----+ +--
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+--+ +-----+ +--+ +--+ +-----+
|#1|#2 |#3 |#4|#5|#6 |#7|#8 |#9 |#10 ...
+--+-----+-----+--+--+-----+--+-----+-----+--
1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, ...
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The first terms of this sequence are:
+-----+--+ +-----+ +-----+--
| . | | | | .
+--+ . +-----+--+ +--+ .
|#1|#2 .#3|#4 .#5|#6 |#7|#8 .#9 ...
+--+-----+--+-----+--+-----+--+-----+--
1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, ...
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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