A113136 - OEIS

%I #15 Mar 21 2020 04:06:26

%S -1,0,1,-2,-1,1,2,-3,-3,-2,-1,1,2,3,3,-4,-4,-3,-1,1,3,4,4,-5,-5,-5,-5,

%T -4,-3,-2,-1,1,2,3,4,5,5,5,5,-6,-6,-5,-1,1,5,6,6,-7,-7,-7,-7,-7,-7,-6,

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

%N The rational numbers can be ordered by height and then by magnitude (see A002246, A097080); sequence gives numerators.

%D M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7.

%H <a href="/index/Ra#rational">Index entries for sequences related to enumerating the rationals</a>

%e The rationals with this ordering, with those of height k in row k (there are three of height 1, and 4*A000010(k) rationals of height k, for k>1):

%e -1 0 1

%e -2 -1/2 1/2 2

%e -3 -3/2 -2/3 -1/3 1/3 2/3 3/2 3

%e -4 -4/3 -3/4 -1/4 1/4 3/4 4/3 4

%e ...

%Y Cf. A113137, A002246, A097080.

%K sign,easy,tabf

%O 1,4

%A _N. J. A. Sloane_, Nov 02 2008

%E More terms from _John W. Layman_, Nov 06 2008