Numerical semigroups of coated odd elements

A numerical semigroup $S$ is coated with odd elements (Coe-semigroup), if $\{x-1,x+1\}\subseteq S$ for all odd element $x$ in $S$. In this note, we will study this kind of numerical semigroups. In particular, we are interested in the study of the Frobenius number, gender and embedding dimension of a numerical semigroup of this type.