are. In other words, G is calculated in 64 steps: the first step is to calculate g 1 with four up-arrows between 3s; the second step is to calculate g 2 with g 1 up-arrows between 3s; the third step is to calculate g 3 with g 2 up-arrows between 3s; and so on, until finally calculating G = g 64 with g 63 up-arrows between 3s. Equivalently, and the superscript on f indicates an iteration of the function , e.g., f 4 ( n ) = f ( f ( f ( f ( n )))) . Expressed in terms of the family of hyperoperations , the function f is the particular sequence , which is a version of the rapidly growing Ackermann function A ( n , n ). (In fact, for all n .) The function f can also be expressed in Conway chained arrow notation as , and this notation also provides the following bounds on G : To convey the difficulty of appreciating the enormous size of Graham's number, it may be helpful to express—in terms of exponentiation alone—just the first term ( g 1 ) of the rapidly growing 64-term sequence. First, in terms of tetration ( ) alone: where the number of 3s in the expression on the right is Now each tetration ( ) operation reduces to a "tower" of exponentiations ( ) according to the definition Thus, becomes, solely in terms of repeated "exponentiation towers", and where the number of 3s