  We give two trees allowing to represent all positive rational numbers. These
trees can be seen as ternary and quinary analogues of the Calkin-Wilf tree. For
each of these two trees, we give recurrence formulas allowing to compute the
rational number corresponding to the node n. These are analogues of the
formulas given by Donald Knuth and Moshe Newman for the Calkin-Wilf tree.
Finally, we show that the two sequences we have obtained, together with
Calkin-Wilf sequence, are the only ones which satisfy a relation analogue to
Newman's relation and enumerate the positive rationals.
