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Search: id:A133117
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| A133117 |
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Fractal sequence based on comparision of {n * tau} with {i*tau} for i = 1 to F(2j) where F(2j) equals the first i for which {n*tau} <= {i*tau} as i goes from 1 to F(2j+2)-1 and F(2j) equals the insertion point of n into P(n-1). The fractional parts {i*tau} are all less than or equal to {F(2j-2)*tau} for 0 < i < F(2j), so there is no chance that an insertion point greater than n in the permutation of the first n-1 integers will be specified by this rule. The table, A132827, gives the insertion points for each n into the permutation P(n-1) of the first n integers. |
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+0
2
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| 1, 2, 1, 2, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 3, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 8
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence is a modification of that in A054065 which gives the fractal series of the same permutation as the permutation of A132917 for which a couple of generating algorithms are given.
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FORMULA
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See A132827.
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EXAMPLE
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The first few permutations are 1, 21, 213, 4213, 54213, 546213 since {6*tau} is greater than {1*Tau} but less than {3*Tau}; and since of 0<i<7 only {3*tau} and {6*tau} are greater than {1*tau}
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CROSSREFS
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Cf. A054065, A132827, A132917, A132828.
Sequence in context: A029197 A029174 A058753 this_sequence A051276 A137752 A081169
Adjacent sequences: A133114 A133115 A133116 this_sequence A133118 A133119 A133120
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KEYWORD
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nonn,uned
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AUTHOR
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Kenneth J Ramsey (Ramsey2879(AT)msn.com), Sep 13 2007
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