It sound like you have admitted that there are patterns in each series to itself, but that you were unable, for whatever the cause, to use that same pattern for another series.
Since you were able to find a pattern in the series, and that each series has patterns that predict what the future will be in that series, it seems to me the claim is verified.
I imagine that a good mathematician could find some sort of pattern between the first entry of series 1, 2, 3, etc, until they repeat again. In fact, since the eclipses repeat, we know that the first entry of series 2 will repeat, if we go through them all in sequential border, so there must be a pattern in some manner.
3.. 78000... 23... 17... 78001... is a pattern.