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A037161
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Well-order the rational numbers; take numerators.
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4
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0, -1, 1, -2, -1, 1, 2, -3, -1, 1, 3, -4, -3, -2, -1, 1, 2, 3, 4, -5, -1, 1, 5, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, -7, -5, -3, -1, 1, 3, 5, 7, -8, -7, -5, -4, -2, -1, 1, 2, 4, 5, 7, 8, -9, -7, -3, -1, 1, 3, 7, 9, -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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0,4
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REFERENCES
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W. 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; Numerator[ 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 ((%), numerator)
a037161 n = a037161_list !! n
a037161_list = 0 : map numerator
(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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sign,easy,nice,frac
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AUTHOR
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STATUS
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approved
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