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Search: id:A131388
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| A131388 |
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Conjectured permutation of the positive integers using Rule 1 with a(1)=1. |
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+0
9
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| 1, 2, 4, 3, 6, 10, 8, 5, 11, 7, 12, 19, 14, 22, 16, 9, 18, 28, 20, 31, 21, 33, 24, 13, 26, 40, 27, 15, 30, 46, 32, 17, 34, 52, 36, 55, 38, 58, 39, 60, 42, 64, 44, 23, 47, 25, 48, 73, 50, 76, 51, 78, 54, 82, 56, 29, 59, 88, 57, 89, 61, 92, 63, 96, 66, 100, 68, 35, 70, 106, 72, 37
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture 1: a( ) is a permutation of the positive integers. Conjecture 2: d( ) is a permutation of the integers. The sequence using "Rule 2" (positive before negative) is A131393.
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FORMULA
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Rule 1 ("negative before positive"): define sequences d( ) and a( ) as follows: d(1)=0, a(1)=1 and for n>=2, d(n) is the greatest negative integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1), or, if no such d exists, then d(n) is the least positive integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1). Then a(n)=a(n-1)+d.
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EXAMPLE
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a(2)=1+1, a(3)=a(2)+2, a(4)=a(3)+(-1), a(5)=a(4)+3, a(6)=a(5)+4.
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CROSSREFS
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Cf. A131389, A131390, A131391, A131392, A131393, A131394, A131395, A131396, A131397.
Sequence in context: A113233 A051849 A083673 this_sequence A131393 A002326 A064273
Adjacent sequences: A131385 A131386 A131387 this_sequence A131389 A131390 A131391
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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), Jul 05 2007
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