A037161 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

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

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 *)

PROG

(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

CROSSREFS