Wilf's question in numerical semigroups S₃ revisited and inequalities for higher genera

We consider numerical semigroups S₃ = d₁,d₂,d₃, minimally generated by three positive integers. We revisit the Wilf question in S₃ and, making use of identities for degrees of syzygies of such semigroups, give a short proof of existence of an affirmative answer. We find also the lower bound for Frobenius numbers of S₃ and upper and lower bounds for higher genera.