Fun math question. Witch’s cauldron in discrete mathematics

  1. There are two cauldrons, A and B.
  2. Place the Number 1 in either cauldron A or B. Then, place the Number 2 in a cauldron. Then 3, 4, …, n.
  3. If two numbers in a cauldron sum up to another number in their cauldron, the game is over.

Whats the maximum number of f(n)?