A037161 Well-order the rational numbers; take numerators.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy
• nice
• frac

References

• W. Sierpiński, Cardinal and Ordinal Numbers, Warsaw 1965, 2nd ed., p. 40.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A037162.

Cf. A020652.

Programs

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]
-- Reinhard Zumkeller, Mar 08 2013

Mathematica

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 *)