I calculated out what the experience needed for each level up to level 20 should be, based on an algorithm that seems to be accurate from what I've seen: to reach level n you need an amount of experience equal to the amount you needed to reach level (n-1) plus a quarter of the total amount of experience you've earned so far. My findings assume that you level as soon as you reach zero exp needed for next level, without going over. The level is listed plus the amount of experience needed to get there.