A037162 Well-order the rational numbers; take denominators.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• frac

References

• 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. A037161.

Cf. A038567.

Programs

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]
-- 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; Denominator[ Flatten[ Table[ order[n], {n, 0, 10}]]] (* Jean-François Alcover, Jun 27 2012 *)