You will find a few things here: http://oeis.org/A000120 On Wed, Jun 1, 2016 at 8:10 PM, Erich Friedman <erichfriedman68@gmail.com> wrote:
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?
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