Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α ? p/q| <(Lq2 )?1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {lp/q : p/q ∈ Q ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) ? C(0) is equal to the sum of all numbers 3 ? lp/q where the Farey index p/q is less than α.