If {Ln} is a sequence defined by Ln = min {Ln-a +Ln-b, Ln-c +Ln-d}, with a, b, c, d positive integers, then one can ask if necessarily Ln = Ln-b + Ln-b, for all sufficiently large n.

The answer is yes if a and b are relatively prime, Ln > 0 initially, and λ < μ, where λ-a + λ-b = 1, μ-c + μ-d = 1. The answer is no if instead a and b have greatest common divisor k ≥2, with c ≡ 0 (mod k), d ≢ 0 (mod k).