Statement

Your professor has just introduced you to the different bases in which a number can be written and wants to test your understanding. His favourite number is 23 (this should not surprise you too much… it is a prime number!) and for this reason his favourite bases are 2 and 3. A number is called special if and only if the sum of the digits of its base two representation is the same as the sum of the digits of its base three representation. Consider the number 6_(10) (the subscript denotes the basis) = 110_(2) = 20_(3). The sum of the digits in base two is 1 + 1 + 0 = 2, which is exactly the sum of the digits in base three: 2 + 0 = 2. Thus, number 6_(10) is special. On the contrary, the number 9_(10) = 1001_(2) = 100_(3) is not special (the sums of digits are 2 and 1, respectively). In order to keep the class busy without much work on his side, your professor has come up with a boring homework assignment...