:: - Discussion

Professor nitwit obtains a hash number of a given positive integer > 3 as follows. He substracts 2 from the number (to get the new number), and multiplies the new number by 2 to get a term. He repeats this with the new number (to get newer numbers and terms) until the number becomes 2 or 1. The hash is defined as the sum of all the numbers generated in the process.
For example, with the number 5, he multiples (5-2 = 3) by 2 to get the first term 6. He multiplies (3 - 2 = 1) by 2 to get the second term 2. As the number has become 1, he stops. The hash is the sum of the two numbers (6+2) = 8.
If Professor Nitwit is given 3 numbers 19, 7, 15, what is the sum of the hash numbers he obtains for the three numbers?