If the stars should appear one night in
a thousand years, how would men believe
and adore, and preserve for many
generations the remembrance of the city
of God?

Ralph Waldo Emerson

An interesting short story written by Isaac Asimov that later became a novel. It explores what would happen to the people living on a planet that is exposed to starlight only once every 2049 years.

Asimov describes the solar system in the novel and short story just enough to make it seem plausible.

This inspired 2 researchers in India to write a paper exploring the possibility of this hypothetical system’s existence; they concluded that it was plausible for the system to exist for at least a couple hundred years.

More research is necessary, using modern solar system simulation techniques.