Hello everyone, I made one experiment with n*n*phi, phi being the golden ratio. I use a precision of let's say 1000 digits and n = 1 to 16000000. If we look at the square grid made of the numbers (without the decimal point), there are no clear patterns in the lines of digits BUT there is a definite pattern in vertical. for each k (from 1 to 1000) I constructed 1 image made out of the first 16 000 000 digits , making one image of 4000 x 4000. This is the result : http://plouffe.fr/phi_time_n_n%20vertical_base_10/index.html These digits are in base 10, so I used a colourization with blue tones : light blue = 0 , darker blue = 9. The thing is : there is a pattern for every k. Very definite pattern. I used that color because in gray scale it does not comes out clearly enough, the colourization. if we take another constant like pi, e, gamma or even a large rational, the same patterns appear, not surprising. Now, the good question is : ok there is a pattern , then what, what is the difference in those patterns. If n*n*n is used instead of n*n, the same but it does scramble after a few digits. Any explanation for such patterns ? best regards, Simon Plouffe