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A072403
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Numerator of the Reingold-Tarjan sequence, denominator=A072404.
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2
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1, 2, 5, 4, 11, 10, 1, 8, 23, 22, 7, 20, 19, 2, 17, 16, 47, 46, 5, 44, 43, 14, 41, 40, 13, 38, 37, 4, 35, 34, 11, 32, 95, 94, 31, 92, 91, 10, 89, 88, 29, 86, 85, 28, 83, 82, 1, 80, 79, 26, 77, 76, 25, 74, 73, 8, 71, 70, 23, 68, 67, 22, 65, 64, 191, 190, 7
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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The Reingold-Tarjan sequence is based on the following function defined on even positive integers and range of the rational numbers:
f(2*n) = if n is even then 2*f(n)/3 else (f(n+1)+f(n-1))/3 for n>1, f(2*1)=1.
f(2*n) = a(n)/A072404(n) for n>1, a(1)=1 and A072404(1)=1.
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REFERENCES
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J.-P. Allouche and J. Shallit, The ring of k-regular sequences (Example 33), Theoretical Computer Science, 98 (1992), 163-197.
E. M. Reingold and R. E. Tarjan, On a greedy heuristic for complete matching, SIAM J. Computing 10 (1981), 676-681.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.
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FORMULA
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A072403(n) / a(n) = 1 - sum(1 / A000244(A029837(k)): k = 1..n). - Reinhard Zumkeller, Jan 01 2013
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PROG
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(Haskell)
import Data.Ratio ((%), denominator)
a072404 n = a072404_list !! (n-1)
a072404_list = map denominator $
scanl1 (-) $ map ((1 %) . a000244) $ a029837_list
-- Reinhard Zumkeller, Jan 01 2013
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CROSSREFS
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Sequence in context: A180338 A100710 A069913 * A010078 A074639 A002314
Adjacent sequences: A072400 A072401 A072402 * A072404 A072405 A072406
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KEYWORD
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nonn,frac
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AUTHOR
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Reinhard Zumkeller, Jun 16 2002
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STATUS
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approved
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