  In the framework of a recently developed model of interacting composite
fermions restricted to a single level, we calculate the activation gaps of a
second generation of spin-polarized composite fermions. These composite
particles consist each of a composite fermion of the first generation and a
vortex-like excitation and may be responsible for the recently observed
fractional quantum Hall states at unusual filling factors such as
nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the
second generation are found to be more than one order of magnitude smaller than
those of the first generation, these states are less visible than the usual
states observed at filling factors nu=p/(2ps+1). Their stability is discussed
in the context of a pseudopotential expansion of the composite-fermion
interaction potential.
