You Do Need power plug adapter while traveling from Luxembourg to Central African Republic.

Here is Why You Need An Adapter

The outlet and plug type used in Central African Republic are C and E and in Luxembourg are C and F. This is how they look like.

Luxembourg

In Luxembourg, outlets of type C and F are in use.

Type C

Type F

Central African Republic

In Central African Republic, outlets of type C and E are in use.

Type C

Type E