Recursive functions of one variable

“The excess function, defined on nonnegative integers, gives, for each n, the excess over the largest perfect square below n, i.e. n − [pn]2. If f maps natural numbers to natural numbers, and takes all possible values, then the inverse of f is also defined, and at place n takes i if i is the smallest argument for which f(i) = n. We prove the following nice theorem of J. Robinson. Consider the smallest set S of functions from natural numbers into natural numbers with the following properties: (i) the identity, the successor and the excess functions are in S, (ii) S is closed under composition and taking inverse. Then S is the set of recursive functions of one variable.”