Sequences of Milnor numbers of deformations of semi-quasi-homogeneous plane curve singularities

Consider a semi-quasi-homogeneous complex plane curve singularity f with Milnor number μ(f). In Theorem 1.1 we list integers which can be attained as Milnor numbers of deformations of the given semi-quasi-homogeneous singularity. The result follows mainly from combinatorial considerations and geometric interpretation of Euclid’s algorithm via the classic relation between Milnor and Newton numbers.