  The aim of the article is to study the Betti numbers of the tangent cone of
Gorenstein monomial curves in affine 4-space. If $C_S$ is a non-complete
intersection Gorenstein monomial curve whose tangent cone is Cohen-Macaulay, we
show that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).
