Search: id:A113137
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%I A113137
%S A113137 1,1,1,1,2,2,1,1,2,3,3,3,3,2,1,1,3,4,4,4,4,3,1,1,2,3,4,5,5,5,5,5,5,5,5,
%T A113137 4,3,2,1,1,5,6,6,6,6,5,1,1,2,3,4,5,6,7,7,7,7,7,7,7,7,7,7,7,7,6,5,4,3,2,
%U A113137 1,1,3,5,7,8,8,8,8,8,8,8,8,7,5,3,1,1,2,4,5,7,8,9,9,9,9,9,9,9,9,9,9,9,9
%N A113137 The rational numbers can be ordered by height and then by magnitude (see 
               A002246, A097080); sequence gives denominators.
%D A113137 M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; 
               p. 7.
%e A113137 The rationals with this ordering, with those of height k in row k (there 
               are 4*A000010(k) rationals of height k, for k>1):
%e A113137 -1 0 1
%e A113137 -2 -1/2 1/2 2
%e A113137 -3 -3/2 -2/3 -1/3 1/3 2/3 3/2 3
%e A113137 -4 -4/3 -3/4 -1/4 1/4 3/4 4/3 4
%e A113137 ...
%Y A113137 Cf. A113136, A002246, A097080.
%Y A113137 Sequence in context: A004739 A156282 A120423 this_sequence A075402 A088855 
               A034851
%Y A113137 Adjacent sequences: A113134 A113135 A113136 this_sequence A113138 A113139 
               A113140
%K A113137 nonn,easy,tabf
%O A113137 1,5
%A A113137 N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2008
%E A113137 More terms from John W. Layman (layman(AT)math.vt.edu), Nov 06 2008

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