Molecular wires of the acene-family can be viewed as a physical realization of a two-rung ladder Hamiltonian. For acene-ladders, closed-shell ab initio calculations and elementary zone-folding arguments predict incommensurate gap oscillations as a function of the number of repetitive ring units, NR, exhibiting a period of about ten rings. Results employing open-shell calculations and a mean-field treatment of interactions suggest anti-ferromagnetic correlations that could potentially open a large gap and wash out the gap oscillations. Within the framework of a Hubbard model with repulsive on-site interaction, U, we employ a Hartree-Fock analysis and the density matrix renormalization group to investigate the interplay of gap oscillations and interactions. We confirm the persistence of incommensurate oscillations in acene-type ladder systems for a significant fraction of parameter space spanned by U and NR.