  We employ the (dynamical) density matrix renormalization group technique to
investigate the ground-state properties of the Bose-Hubbard model with
nearest-neighbor transfer amplitudes t and local two-body and three-body
repulsion of strength U and W, respectively. We determine the phase boundaries
between the Mott-insulating and superfluid phases for the lowest two Mott lobes
from the chemical potentials. We calculate the tips of the Mott lobes from the
Tomonaga-Luttinger liquid parameter and confirm the positions of the
Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find
that physical quantities in the second Mott lobe such as the gap and the
dynamical structure factor scale almost perfectly in t/(U+W), even close to the
Mott transition. Strong-coupling perturbation theory shows that there is no
true scaling but deviations from it are quantitatively small in the
strong-coupling limit. This observation should remain true in higher dimensions
and for not too large attractive three-body interactions.
