An Unexpected Sequence

Warm Up:

I have some candy and you have some candy.  I give you one of my candies.  You now have twice as much as me.  You give me one candy back.  We now have the same amount.

How many candies did we both start with?

Main Event

What do you think is the next number in the sequence below?

10^3, 10^9, 10^{27}, 10^2