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Search: id:A089215
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| A089215 |
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Thue-Morse sequence on the integers. |
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+0
1
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| 1, 2, 3, 2, 4, 3, 2, 3, 5, 4, 3, 4, 2, 3, 4, 3, 6, 5, 4, 5, 3, 4, 5, 4, 2, 3, 4, 3, 5, 4, 3, 4, 7, 6, 5, 6, 4, 5, 6, 5, 3, 4, 5, 4, 6, 5, 4, 5, 2, 3, 4, 3, 5, 4, 3, 4, 6, 5, 4, 5, 3, 4, 5, 4, 8, 7, 6, 7, 5, 6, 7, 6, 4, 5, 6, 5, 7, 6, 5, 6, 3, 4, 5, 4, 6, 5, 4, 5, 7, 6, 5, 6, 4, 5, 6, 5, 2, 3, 4, 3, 5, 4, 3, 4, 6
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OFFSET
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1,2
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COMMENT
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S(1)={1,2} then M(1)=4 and S'(1)={4-1,4-2}={3,2}. So S(2)={1,2,3,2}. M(2)=5 so S(3)={1,2,3,2}{5-1,5-2,5-3,5-2} and sequence begins 1,2,3,2,4,3,2,3,..
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FORMULA
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sum(k=1, n, a(k)) is asymptotic to C*n*log(n) with C=0.8....
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EXAMPLE
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Sequence is S(infinity) where S(1)={1,2} and S(n+1)=S(n)S'(n) where S'(n) is obtained from S(n) by substituting an element x of S(n) with M(n)-x where M(n)=2+Max(S(n)}. Thue-Morse sequence on alphabet {1,2}is constructed as follows: S(1)={1,2} and S(n+1)=S(n)S'(n) where S'(n) is obtained from S(n) by substituting an element x of S(n) with 3-x
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CROSSREFS
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Cf. A001285.
Sequence in context: A058973 A105117 A100876 this_sequence A070296 A072645 A135817
Adjacent sequences: A089212 A089213 A089214 this_sequence A089216 A089217 A089218
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 10 2003
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