Let f be a primitive recursive total function, and let A be the set of all n such that the value f(n) is 'new' in the sense of being different from f(m) for all m<n. Show that A is primitive recursive. How in the world do I attack this problem? I am totally lost. Any help would be greatly appreciated. Thanks. I know that to show a set is primitive recursive the characteristic function of the set must be primitive recursive. What in the world, however, would be a suitable characteristic function for this set described above?