1. Among the seven points consisting of the center and the six vertices of a regular hexagon, if any $n$ points are taken, and among them, there must be three points that form the vertices of an equilateral triangle, then the minimum value of $n$ is $\qquad$
-1.5 .
Consider the regular hexagon $A B C D E F$ as shown in Figure 1, with its center at $O$.

When $n=4$, take $A, C, D, F$, among which no three points can form the three vertices of an equilateral triangle.
When $n=5$, consider the following two cases:
(1) $O$ is among the five points. Consider the three pairs of points $(A, B)$, $(C, D)$, $(E, F)$. According to the pigeonhole principle, at least one pair of points must be taken, which, together with the center $O$, can form the three vertices of an equilateral triangle.
(2) $O$ is not among the five points. Consider the two groups of points $(A, C, E)$ and $(B, D, F)$. According to the pigeonhole principle, at least one group of points must be taken, which can form the three vertices of an equilateral triangle.
In summary, the minimum value of $n$ is 5.