I remember that the recursion

$r(0)=0, \ \ r(n+1)=\frac{1}{2 [r(n)]+1-r(n)}$ produces a sequence of rational values $ 0 \mapsto 1 \mapsto 1/2 \mapsto 2 \mapsto 1/3 \mapsto ... $ which exausts the positive fractions (and of course every fraction can only appear once).

Unfortunately I do not remember the reference for this statement. Can anybody help me?