Enumerating the Rationals from Left to Right
S. P. Glasby · American Mathematical Monthly · 2011
The rationals can be enumerated using Stern-Brocot sequences 풮ℬn, Calkin-Wilf sequences 풞풲n, or Farey sequences ℱn. We show that the rationals in 풮ℬn, 풞풲n, and ℱn can be computed using very similar second-order linear recurrence relations. (This, incidentally, obviates the need to compute previous sequences 풮ℬi, 풞풲i, ℱi with i < n.)