There isn't an algorithm that solves all possible questions like this: you need to develop some good "instinct" to see a solution.
In this case, you can see that each number is twice the previous one, plus one.
So, you start from 3. Double it (6) and add 1, you get 7.
Double it (14) and add 1, you get 15.
And so on...
So, if you are at 63, you have to double it (126) and add 1 to get 127.
