A113136 The rational numbers can be ordered by height and then by magnitude (see A002246, A097080); sequence gives numerators.

-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, -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, -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

Offset

1,4

References

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

Links

Table of n, a(n) for n=1..83.

Index entries for sequences related to enumerating the rationals

Example

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):
-1 0 1
-2 -1/2 1/2 2
-3 -3/2 -2/3 -1/3 1/3 2/3 3/2 3
-4 -4/3 -3/4 -1/4 1/4 3/4 4/3 4
...

Crossrefs

Cf. A113137, A002246, A097080.

Sequence in context: A328062 A326281 A343026 * A156267 A160325 A054989

Adjacent sequences: A113133 A113134 A113135 * A113137 A113138 A113139

Keyword

sign,easy,tabf

Author

N. J. A. Sloane, Nov 02 2008

Extensions

More terms from John W. Layman, Nov 06 2008

Status

approved