**n**in a circle and then writing

**G(n)**in a circle below it and connecting the two circles with a line. It ends up looking sort of like a tree. Try it yourself if you want.

[tex] G(n) = n - G(G(n-1)) [/tex] for n>0. G(0)=0

You start with n=2 in a circle to make the tree. Now suppose you flipped the tree as if in a mirror and renumbered the circles increasing from left to right, starting with the lowest circles. The challenge is to find an algebraic definition for this new tree. If you place F(n) beneath n then the equations you get are:

F(2)=1

F(3)=2

F(4)=3

F(5)=3

F(6)=4

F(7)=5

F(8)=5

F(9)=6

F(10)=6

F(11)=7

F(12)=8

F(13)=8

F(14)=9

F(15)=10

F(16)=10

F(17)=11

F(18)=11

F(19)=12

F(20)=13

F(21)=13

If you can figure out F(n) please point me in the right direction.