A113137 The rational numbers can be ordered by height and then by magnitude (see A002246, A097080); sequence gives denominators.

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, 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, 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

Offset

1,5

References

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

Links

Table of n, a(n) for n=1..105.

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 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. A113136, A002246, A097080.

Sequence in context: A343559 A242357 A120423 * A220603 A238404 A331910

Adjacent sequences: A113134 A113135 A113136 * A113138 A113139 A113140

Keyword

nonn,easy,tabf

Author

N. J. A. Sloane, Nov 02 2008

Extensions

More terms from John W. Layman, Nov 06 2008

Status

approved