Sometimes these weird questions can lead to more practical applications down the road, e.g. once we know how to do something it gets added to the toolbox and ev

Sometimes these weird questions can lead to more practical applications down the road, e.g. once we know how to do something it gets added to the toolbox and eventually used, somewhat like how Euler's totient was a cute mathemtatical curiosity until it became one of the important steps in RSA key generation and a very useful tool almost two centuries after it was discovered. It is also the case that sometimes knowing where the 'holes' are in these sort of stepwise math series' can itself reveal something deeper or more important. Like the fabled exceptions that prove the rule, knowing where a general rule does not work is sometimes an incredibly useful discovery.