Question 23
There is a series of integers: 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, ... , this series has totally 109 numbers, and starting from the third number, each term is sum of the last number before it and twice the second last number before it. If we divide these 109 integers by 7, we get 109 remainders. What is the sum of all these remainders?