Dogstomp

5->2: Two would naturally be the reward for cashing in 6, but if it were, you would have no reason to save past 3. So they discount the cost to 5.

8->3: This is not a special discount number. It's just a combination of 5 (gives 2) + 3 (gives 1).

9->4: The next discount mark would be 10, two 5's, but if they just left it at that, nobody would have any reason to save until 10 over just cashing out on every 5. So how they pulled the cost back from 6 to 5, they pulled the cost back from 10 to 9.

12->5: similar to 8, this reward is just the previous 9 (gives 4) + 3 (gives 1)

14->6: is 5+5+5, with cost pulled back for the same reason as 5 and 9.

17->8: This is just the previous +3, AND the 5 rule combined, because 18 will be 9+9.

20->9: Previous + 3 again

22->10: This one is like a +3 situation but for being 5 more than the PREVOUS previous, 17.