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

Author

N. J. A. Sloane, Nov 02 2008

Keywords

• sign
• easy
• tabf

Examples

			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
...
		

References

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

Links

• Index entries for sequences related to enumerating the rationals

Crossrefs

Cf. A113137, A002246, A097080.

Extensions

More terms from John W. Layman, Nov 06 2008