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A037162
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Well-order the rational numbers; take denominators.
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4
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1, 1, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 5, 5, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 1, 3, 5, 7, 7, 5, 3, 1, 1, 2, 4, 5, 7, 8, 8, 7, 5, 4, 2, 1, 1, 3, 7, 9, 9, 7, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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REFERENCES
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Sierpiński, Cardinal and Ordinal Numbers, Warsaw 1965, 2nd ed., p. 40.
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LINKS
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MATHEMATICA
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order[n_] := Join[-Reverse[ pos = Select[(r = Range[n])/Reverse[r], Numerator[#] + Denominator[#] == n + 1 & ] ], pos]; order[0] = 0; Denominator[ Flatten[ Table[ order[n], {n, 0, 10}]]] (* Jean-François Alcover, Jun 27 2012 *)
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PROG
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(Haskell)
import Data.List (transpose)
import Data.Ratio ((%), denominator)
a037162 n = a037162_list !! n
a037162_list = 1 : map denominator
(concat $ concat $ transpose [map (map negate) qss, map reverse qss])
where qss = map q [1..]
q x = map (uncurry (%)) $ filter ((== 1) . uncurry gcd) $
zip (reverse zs) zs where zs = [1..x]
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CROSSREFS
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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STATUS
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approved
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