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.