It's based on my own in-game observations.
I guess I should tell you all I know:
+20 0
+19 313
+18 452
+17 560-565
+16 655-657
+15 735-738
+14 801
+13 858-866
+12 908-910
+11 952-954
+10 991
+9 1025-1026
+8 1054-1058
+7 1078-1085 (this probably isn't the minimum gain, this is just where I stopped)
I saw that I got +18 at 559 (to 577) and +17 at 565, for example.
I had the chance to note most of that back when I was lv19, and was saving up AP so I could get the lv20 skills quickly. Of course, all the stuff past 313 isn't particularly useful except for curiosity: you mainly need to know what you said earlier about spending enough to always get +20.