Double exponential function

A double exponential function is a constant raised to the power of an exponential function. The general formula is f ( x ) = a b x = a ( b x ) {displaystyle f(x)=a^{b^{x}}=a^{(b^{x})}} , which grows much more quickly than an exponential function. For example, if a = b = 10:Aho and Sloane observed that in several important integer sequences, each term is a constant plus the square of the previous term. They show that such sequences can be formed by rounding to the nearest integer the values of a doubly exponential function in which the middle exponent is two. Integer sequences with this squaring behavior includeIn computational complexity theory, some algorithms take doubly exponential time: