We show that three numerical semigroups $\langle 5, 6, 7, 8\rangle, \langle3, 7, 8\rangle$ and $\langle 3, 5\rangle$ are of double covering type, i.e., the Weierstrass semigroups of ramification points on double covers of curves. Combining the result with  and  we can determine the Weierstrass semigroups of the ramification points on double covers of genus two curves.
"The Weierstrass semigroups on double covers of genus two curves." Tsukuba J. Math. 38 (2) 201 - 206, March 2015. https://doi.org/10.21099/tkbjm/1429103721