A037161 - OEIS

%I #14 Dec 20 2014 03:03:44

%S 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,

%T -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,

%U -9,-7,-3,-1,1,3,7,9,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1

%N Well-order the rational numbers; take numerators.

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

%H Reinhard Zumkeller, <a href="/A037161/b037161.txt">Table of n, a(n) for n = 0..10000</a>

%t 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 *)

%o (Haskell)

%o import Data.List (transpose)

%o import Data.Ratio ((%), numerator)

%o a037161 n = a037161_list !! n

%o a037161_list = 0 : map numerator

%o   (concat $ concat $ transpose [map (map negate) qss, map reverse qss])

%o   where qss = map q [1..]

%o         q x = map (uncurry (%)) $ filter ((== 1) . uncurry gcd) $

%o                   zip (reverse zs) zs where zs = [1..x]

%o -- _Reinhard Zumkeller_, Mar 08 2013

%Y Cf. A037162.

%Y Cf. A020652.

%K sign,easy,nice,frac

%O 0,4

%A _N. J. A. Sloane_