Try this (Score 1)

Try this, the numbers start with the 2,6,24,100 digit so do g(x)=y there the y values are the indexes to get g(1)=2 g(2)=6 g(3)=24 g(4)=100, then for fun divide y by x to get 2,3,8,25 and notice the
g(x)=(g(x-1)*g(x-2))+(5-x) pattern 2,3,8,25,400,9999,... so then g(5)= 5(400)
so its the 10 digit number starting at the 2000 index so its f(5)=3955990067. I guess google did not see that one.