  We define the concentration of a numerical semigroup $S$ as
$\mathsf{C}(S)=\max \left\{\text{next}_S(s)-s ~|~ s\in S \backslash
\{0\}\right\}$ wherein $\text{next}_S(s)=\min\left\{x \in S ~|~ s<x\right\}$.
In this paper, we study the class of numerical semigroups with concentration
$2$. We give algorithms to calculate the whole set of this class of semigroups
with given multiplicity, genus or Frobenius number. Separately, we prove that
this class of semigroups verifies the Wilf's conjecture.
