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Search: id:A162912
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| A162912 |
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Denominators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree. |
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+0
3
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| 1, 2, 1, 3, 1, 3, 2, 5, 2, 4, 3, 4, 1, 5, 3, 8, 3, 7, 5, 5, 1, 7, 4, 7, 3, 5, 4, 7, 2, 8, 5, 13, 5, 11, 8, 9, 2, 12, 7, 9, 4, 6, 5, 10, 3, 11, 7, 11, 4, 10, 7, 6, 1, 9, 5, 12, 5, 9, 7, 11, 3, 13, 8, 21, 8, 18, 13, 14, 3, 19, 11, 16, 7, 11, 9, 17, 5, 19, 12, 14, 5, 13, 9, 7, 1, 11, 6, 17, 7, 13, 10, 15
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OFFSET
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1,2
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COMMENT
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The drib tree is an infinite binary tree labelled with rational numbers. It is generated by the following iterative process: start with the rational 1; for the left subtree increment and then reciprocalise the current rational; for the right subtree interchange the order of the two steps: the rational is first reciprocalised and then incremented. Like the Stern-Brocot and the Bird tree, the drib tree enumerates all the positive rationals (A162911(n)/A162912(n)).
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REFERENCES
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R. Hinze, The Bird tree, Journal of Functional Programming 19(5), 2009. To appear.
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FORMULA
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b(n) where a(1) = 1; a(2n) = b(n); a(2n+1) = a(n) + b(n); and b(1) = 1; b(2n) = a(n) + b(n); b(2n+1) = a(n);
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EXAMPLE
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The first four levels of the drib tree: [1/1] [1/2, 2/1] [2/3, 3/1, 1/3, 3/2], [3/5, 5/2, 1/4, 4/3, 3/4, 4/1, 2/5, 5/3]
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PROGRAM
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(Other) import Ratio; drib :: [Rational]; drib = 1 : map (recip . succ) drib \/ map (succ . recip) drib; (a : as) \/ bs = a : (bs \/ as); a162911 = map numerator drib; a162912 = map denominator drib
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CROSSREFS
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This sequence is the composition of A162910 and A059893: a(n) = A162910(A059893(n)). This sequence is a permutation of A002487(n+2).
Sequence in context: A007735 A002616 A046073 this_sequence A039776 A048864 A003139
Adjacent sequences: A162909 A162910 A162911 this_sequence A162913 A162914 A162915
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Ralf Hinze (ralf.hinze(AT)comlab.ox.ac.uk), Aug 05 2009
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