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

Here is Why You Need An Adapter

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

Central African Republic

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

Type C

Type E

Nauru

In Nauru, outlets of type I are in use.

Type I