The iterated power function is the function such that:
  • n ^^ 0 = 1
  • n ^^ m = n**(n^^(m-1))
For example, 2^^1 = 2, 2^^2 = 2**2 = 4, 2^^3 = 2**(2**2) = 16, 2^^4 = 2**(2**(2**2)) = 65536, and so on.

The ^^ notation is due to Donald Knuth: a^n is the normal power (exponentiation) operation, so a^^n is the iterated power.

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