Guess the calendar question

I was asked a very good question in response to my previous post. Can you guess it?

I was asked a somewhat related question in response to my last post (about haftorahs that are rarely read on consecutive years). I answered with the above screenshot. Can you guess the question?

Additionally, the only other instance I found was so long ago that John Qunicy Adams was president at the time:

Hopefully at some point (if not soon, definitely before Rosh Hashanah 2024) I’ll elaborate on this phenomenon.