Calkin–Wilf tree
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number 1, and any rational number q expressed in simplest terms as the fraction a/b has as its two children the numbers 1/1+1/q = a/a + b and q + 1 = a + b/b.