  We construct clusters of bound particles for a quantum integrable derivative
delta-function Bose gas in one dimension. It is found 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. Interestingly, there exists a connection between the
above mentioned 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 for the derivative
delta-function Bose gas and the determination of various properties of these
clusters like their size and their stability under a variation of the coupling
constant.
