How to repeat automatic, or full: three selected one skip mesh edge?
Use Checker Deselect to deselect some edges and leave others selected according to the pattern.
To make it run properly select the full ring of edges where are located those shown on your screenshot. If you want complete ring of edges selected then press Ctrl+Alt and click with RMB on the edge.
Make sure to choose active edge as in the screenshot (it is marked with red color, the leftmost one), so it corresponds to those which should be left selected.
Then execute Checker Deselect. Set its properties so it deselects every 2nd element and preserves the pattern of 3 edges together. Set the starting point of the selection with Offset, in this case it's 2.