[seqfan] Recounting the rationals

[Joshua Zucker]

Finding ways of labeling the rationals is always a fun game.

Harold Reiter just showed me a whole family of ways to recount the
rationals (actually, in general, to find a 1-1 correspondence between
either the lattice quarter-plane or the whole lattice plane and the
nonnegative integers).

I figure I should pick a few of the most "natural" ways in the family,
write them up for OEIS, and for each one, give:
The sequence of x coordinates of the points (numerators of the fractions),
the sequence of y coordinates (denominators),
and then conversely, label each point in the plane with its natural
number, and treat that as a tabl sequence read by diagonals.

Does this seem sensible?  Are there any other ways I should submit
these?  And when it's the whole lattice plane, what could/should be
the tabl analogue for how to submit the sequence?

Thanks,
--Joshua Zucker