Three more than a number is less than twice the number.

Assume that the number you are looking for is n.

Now, three more than the number can be written as: n + 3

twice the number is 2n.

Therefore, transforming the given condition into an equation, we get:

3 + n < 2n

3 < 2n - n

3 < n

Therefore, the number you are looking for could be any number greater than three.