Here are the first 800 numbers of the series plotted in this 800 pixel wide image. The height of each is rounded to the nearest pixel.
(You really have to click and zoom in to be able to see the pattern)
Isn't that interesting there is a clear regularity to the pattern but I have verified that the heights of any two of these pixels are no closer than .005 apart. That means in the first 800 of the series you never repeat exactly a value. So it can't be a simple repetitive pattern.