Let k ≥ 2 and define F (k) := (F (k) n )n≥0, the k-generalized Fibonacci sequence whose terms satisfy the recurrence relation F (k) n = F (k) n−1 + F (k) n−2 + . . . + F (k) n−k , with initial conditions 0, 0, . . . , 0, 1 (k terms) and such that the first nonzero term is F (k) 1 = 1. The sequences F := F (2) and T := F (3) are the known Fibonacci and Tribonacci sequences, respectively. In 2005, Noe and Post made a conjecture related to the possible solutions of the Diophantine equation F (k) n = F (l) m . In this note, we use transcendental tools to provide a general method for finding the intersections F (k) ∩F (m) which gives evidence supporting the Noe-Post conjecture. In particular, we prove that F ∩ T = {0, 1, 2, 13}.