%I A038569
%S A038569 1,2,1,3,1,3,2,4,1,4,3,5,1,5,2,5,3,5,4,6,1,6,5,7,1,7,2,7,3,7,4,7,5,7,6,
%T A038569 8,1,8,3,8,5,8,7,9,1,9,2,9,4,9,5,9,7,9,8,10,1,10,3,10,7,10,9,11,1,11,2,
%U A038569 11,3,11,4,11,5,11,6,11,7,11,8,11,9,11,10,12,1,12,5,12,7,12,11,13,1,13
%N A038569 Denominators in canonical bijection from positive integers to positive 
               rationals.
%D A038569 H. Lauwerier, Fractals, Princeton Univ. Press, p. 23.
%H A038569 David Wasserman, <a href="b038569.txt">Table of n, a(n) for n = 0..100000</
               a>
%H A038569 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%e A038569 First arrange fractions by increasing denominator then by increasing 
               numerator:
%e A038569 1/1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, ... (this is A038566/A038567);
%e A038569 now follow each term by its reciprocal:
%e A038569 1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, ... (this is A038568/
               A038569).
%p A038569 with (numtheory): A038569 := proc (n) local sum, j, k; sum := 1: k := 
               2: while (sum < n) do: sum := sum + 2 * phi(k): k := k + 1: od: sum 
               := sum - 2 * phi(k-1): j := 1: while sum < n do: if gcd(j,k-1) = 
               1 then sum := sum + 2: fi: j := j+1: od: if sum > n then RETURN (k-1) 
               fi: RETURN (j-1): end: # from UlrSchimke(AT)aol.com, Oct 31, 2001
%Y A038569 Cf. A020652, A020653, A038566-A038569.
%Y A038569 Sequence in context: A025808 A144079 A071575 this_sequence A020650 A124224 
               A014599
%Y A038569 Adjacent sequences: A038566 A038567 A038568 this_sequence A038570 A038571 
               A038572
%K A038569 nonn,frac,core,nice
%O A038569 0,2
%A A038569 N. J. A. Sloane (njas(AT)research.att.com).
%E A038569 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).