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Search: id:A141105
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| A141105 |
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Upper Even Swappage of Upper Wythoff Sequence. |
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+0
4
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| 2, 6, 8, 10, 14, 16, 18, 20, 24, 26, 28, 32, 34, 36, 40, 42, 44, 48, 50, 52, 54, 58, 60, 62, 66, 68, 70, 74, 76, 78, 82, 84, 86, 90, 92, 94, 96, 100, 102, 104, 108, 110, 112, 116, 118, 120, 124, 126, 128, 130, 134, 136, 138, 142, 144, 146, 150, 152, 154, 158, 160, 162
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OFFSET
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1,1
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COMMENT
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1. lim (1/n)*A141105(n) = 1 + tau
2. Let S(n)=(1/2)*A141105(n). Is the complement of S equal to A035487?
3. Is A141105 = 1+A141106?
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FORMULA
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Let a = (1,3,4,6,8,9,11,12,...) = A000201 = lower Wythoff sequence; let b = (2,5,7,10,13,15,18,...) = A001950 = upper Wythoff sequence. For each odd b(n), let a(m) be the greatest number in a such that after swapping b(n) and a(m), the resulting new a and b are both increasing. A141105 is the sequence obtained by thus swapping all odds out of A001950.
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EXAMPLE
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Start with
a = (1,3,4,6,8,9,11,12,...) and b = (2,5,7,10,13,15,18,...).
After 1st swap,
a = (1,3,4,5,8,9,11,12,...) and b = (2,6,7,10,13,15,18,...).
After 2nd swap,
a = (1,3,4,5,7,9,11,12,...) and b = (2,6,8,10,13,15,18,...).
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CROSSREFS
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Cf. A000201, A001950, A141104, A141106, A141107, A004976.
Adjacent sequences: A141102 A141103 A141104 this_sequence A141106 A141107 A141108
Sequence in context: A076300 A049637 A075332 this_sequence A047395 A036554 A095736
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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), Jun 02 2008
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