On dual sequences of measurable amounts of the two jugs problem

Let M(m, n) be the integer sequence of all positive measurable amounts less than m + n that are obtainable by two unmarked jugs with capacities m and n units. We introduce the concept of dual sequences which describe the correspondence relation between M (m₁, n₁) and M (m₂, n₂), where 0 < m₁ < n₁, 0 < m₂ < n₂, m₁ + n₁ = m₂ + n₂ and gcd (m₁, n₁) = gcd (m₂, n₂) = 1. Some illustrative examples are provided. Copyright © 2018 Research India Publications.