An extremal problem for subset-sum-distinct sequences with congruence conditions Original Research Article

For a given congruence condition, we try to find a subset-sum-distinct sequence such that the sum of the reciprocals of its terms is maximal. We show that the greedy algorithm generates an extremal sequence infinitely often but also fails to generate an extremal sequence infinitely often. We also provide two criteria for determining whether the sequence provided by the greedy algorithm is maximal or not.