[seqfan] Re: Canonical bijection from positive integers to positive rationals.

[Peter Luschny]

NS> For me, without doubt, the best map is the classic map based
NS> on the Stern's diatomic series (or Stern-Brocot sequence, A002487.

For me it is the Euclid tree: A295515.

NS> from 1858: Look at all the references there.

Let's wait and see. In 160 years, we can count references again.
If you have Maple you can also try this delightful implementation:

    magic := x -> 1/(1 + floor(x) - frac(x)):

And then run:

    0; do magic(%) od;

Cheers, Peter