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Search: id:A078880
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| A078880 |
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The sequence starting with 2 that equals its own run length sequence. |
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2
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| 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It is an unsolved problem to show that the density of 1's is equal to 1/2.
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REFERENCES
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M. S. Keane, Ergodic theory and subshifts of finite type, Chap. 2 of T. Bedford et al., eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford, 1991, esp. p. 50.
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FORMULA
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a(n) = k(n+1), where k=A000002, the Kolakoski sequence.
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EXAMPLE
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Start with 2, which generates 22 (so that the first run length is 2); then 22 generates 2211 (so that the first two run lengths are 2 and 2); then 2211 generates 221121 and so on.
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CROSSREFS
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See A000002, the official version of this sequence, for formulae, references, links, etc.
Sequence in context: A167677 A074293 A013949 this_sequence A000002 A074295 A116514
Adjacent sequences: A078877 A078878 A078879 this_sequence A078881 A078882 A078883
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Dec 11 2002
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