3 ms·

It sounds like you've just found one for >=2: 2, S(2), S(S(2)), ...

• Someone 2y ago
  That, somewhat ironically, typically isn’t included in the set of elementary functions. ‘plus’ is, but ‘plus one’ isn’t.
  • tikhonj 2y ago
    That gets at what makes using additional functions like in the blog post a bit arbitrary: we don't have special notation for "+ 1" or "* 2", but we do for "^(1/2)" and "log_2". It's not hard to imagine a different world where "+ 1" or "^2" had special notation, and suddenly we'd be able to solve the question in even simpler ways. It's still a fun puzzle, it's just based more on our shared notational conventions as much as the underlying math.
    • madcaptenor 2y ago
      For example it would not be weird to have ++ instead of +1.
      • StilesCrisis 2y ago
        That’s just S(n)