Solomon Golomb's “self-describing sequence" (f(1), f(2), f(3), XXXXXXXXXXis the only nondecreasing sequence of positive integers with the property that it contains exactly f(k) occurrences of k...

Solomon Golomb's “self-describing sequence" (f(1), f(2), f(3), . . .) is the only nondecreasing sequence of positive integers with the property that it contains exactly f(k) occurrences of k for each k. A few moments' thought reveals that the sequence must begin as follows:

Let g(n) be the largest integer m such that f(m) = n. Show that