On the Binary Digits of a Power Original Research Article

LetB(m) denote the number of ones in the binary expansion of an integermgreater-or-equal, slanted2. We prove that lim supm→∞ B(mh)/log2 m=hfor integershgreater-or-equal, slanted2. We also prove the same result withmhreplaced by any polynomiala0mh+a1mh−1+…+ahwith integer coefficients anda0>0.