  In this paper we discuss a novel procedure for constructing clusters of bound
particles in the case of a quantum integrable derivative delta-function Bose
gas in one dimension. It is shown that clusters of bound particles can be
constructed for this Bose gas for some special values of the coupling constant,
by taking the quasi-momenta associated with the corresponding Bethe state to be
equidistant points on a single circle in the complex momentum plane. We also
establish a connection between these special values of the coupling constant
and some fractions belonging to the Farey sequences in number theory. This
connection leads to a classification of the clusters of bound particles
associated with the derivative delta-function Bose gas and allows us to study
various properties of these clusters like their size and their stability under
the variation of the coupling constant.
