Presidents who foresaw future Presidents?

[All Along The Watchtower]

I'd like to know which presidents met a sitting president when they were young and not involved in politics yet.

Clinton met JFK as a young man.

George W. Bush obviously did due to his father's political positions and George H. W. Bush likely did for the same reason.

Did Obama? Did Reagan?

Richard Nixon's father always would brag about how President William McKinley once complimented him on his horse, or something.

After that,  Mr. Nixon was a lifelong Republican.