[math-fun] sum of binary digits

Let n be a positive integer. Let g(n) be the sum of the binary digits of n. I am looking for interesting facts involving g(n). Here are 3 that i have so far, in increasing difficulty to prove: Theorem 1: The minimum number of integral powers of 2 to sum to n is g(n). Theorem 2: The highest power of 2 to divide n! is 2^[ n - g(n) ]. Theorem 3: The number of odd entries in the nth row of Pascal's Triangle is 2^[ g(n) ]. Anyone know any others? Erich Friedman