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A037162 Well-order the rational numbers; take denominators.

%I A037162 #11 Mar 06 2015 22:49:39
%S A037162 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,
%T A037162 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,
%U A037162 6,7,8,9,10,10,9,8,7,6,5,4,3,2,1
%N A037162 Well-order the rational numbers; take denominators.
%D A037162 Sierpiński, Cardinal and Ordinal Numbers, Warsaw 1965, 2nd ed., p. 40.
%H A037162 Reinhard Zumkeller, <a href="/A037162/b037162.txt">Table of n, a(n) for n = 0..10000</a>
%t A037162 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 *)
%o A037162 (Haskell)
%o A037162 import Data.List (transpose)
%o A037162 import Data.Ratio ((%), denominator)
%o A037162 a037162 n = a037162_list !! n
%o A037162 a037162_list = 1 : map denominator
%o A037162   (concat $ concat $ transpose [map (map negate) qss, map reverse qss])
%o A037162   where qss = map q [1..]
%o A037162         q x = map (uncurry (%)) $ filter ((== 1) . uncurry gcd) $
%o A037162                   zip (reverse zs) zs where zs = [1..x]
%o A037162 -- _Reinhard Zumkeller_, Mar 08 2013
%Y A037162 Cf. A037161.
%Y A037162 Cf. A038567.
%K A037162 nonn,easy,nice,frac
%O A037162 0,5
%A A037162 _N. J. A. Sloane_