  We consider a tight-binding model on the honeycomb lattice in a magnetic
field. For special values of the hopping integrals, the dispersion relation is
linear in one direction and quadratic in the other. We find that, in this case,
the energy of the Landau levels varies with the field B as E_n(B) ~
[(n+\gamma)B]^{2/3}. This result is obtained from the low-field study of the
tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter
spectrum) as well as from a calculation in the continuum approximation at low
field. The latter links the new spectrum to the one of a modified quartic
oscillator. The obtained value $\gamma=1/2$ is found to result from the
cancellation of a Berry phase.
