say you have:
x_1, x_2, x_3, x_4, x_5 ...
x_1 = sqrt (x_2 - x_1)
x_2 = sqrt (x_3 - x_2)
so x_(n+1) = x_n(x_n + 1)
even try this rule!
x_2 = x_1(x_1+1) = 1*(2) = 2
x_3 = x_2(x_2+1) = 2*(3) = 6
x_4 = x_3(x_3+1) = 6*(7) = 42
ok so I have proved my rule works!
So the next numbers (I'll call x_6, x_7, x_8, x_9) are:
x_6 = x_5(x_5+1) = 1806*1807 = 3,263,442
x_7 = x_6(x_6+1) = 3,263,442*3,263,443 = 1.065x10^13
x_8 = 1.13x10^26
x_9 = 1.286x10^52
therefore the sequence is:
1,2,6,42,1806,3263442,1.065x10^13,1.13x10^26,1.29x10^52
Am I right?