  Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue
on {1,3} can be related to a primitive substitution rule. Using this
connection, we prove that the corresponding bi-infinite fixed point is a
regular generic model set and thus has a pure point diffraction spectrum. The
Kolakoski-(3,1) sequence is then obtained as a deformation, without loosing the
pure point diffraction property.
