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Search: id:A082524
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| A082524 |
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a(1)=1, a(2)=2, then use the rule when a(n) is the end of a run, n appears a(n) times. |
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1
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| 1, 2, 2, 3, 3, 5, 5, 5, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All Fibonacci numbers >=1 occur. For k>=4, the k-th Fibonacci numbers occur F(k-1) times. Sequence n-a(n) consists of (0,0) union successive runs 1,2,...,F(k) k>=1.
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FORMULA
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(n-1)/tau < a(n) < n where tau is the golden ratio; k>=3 a(F(k))=F(k-1) where F(k) is the k-th Fibonacci number.
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EXAMPLE
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Sequence begins 1,2,2 : a(3)=2 is the end of the second run, hence 3 will appear twice and sequence continues : 1,2,2,3,3. Now a(5)=3 is the end of the third run, hence 5 appears 3 times and sequence continues : 1,2,2,3,3,5,5,5, (From Labos, E.)
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CROSSREFS
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Adjacent sequences: A082521 A082522 A082523 this_sequence A082525 A082526 A082527
Sequence in context: A059974 A045767 A108221 this_sequence A099961 A038810 A086609
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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), Apr 30 2003
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