I observed the pattern of this irrational number: $\sqrt{1 + \sqrt{2}}$ and realized that each element $a_i$ occurred very randomly. For the first 100 elements, this is the result:
[1,1,1,4,6,1,2,2,2,1,1,6,1,179,48,1,356,1,1,3,15,2,1,4,8,3,1,1,1,5,1,1,9,1,19,1, 2,13,2,1,1,4,2,1,1,3,2,1,1,4,15,1,4,5,1,7,6,1,6,6,2,3,38,1,4,1,9,3,1,2,1,2,1,2,1 ,1,3,1,4,1,2,4,1,4,1,1,1,58,6,3,4,203,4,14,2,1,1,41,2,2]
As I increase the length of this sequence, the number were even more arbitrary. So I wonder is there any previous work or paper which relates to random number generator using continued fraction approach? Any idea? Thank you.