[Orgmode] The recurring task pattern

[Ivan Nedrehagen]

Hi everyone, I have a pattern that repeats itself in org-mode and I am  
wondering if anyone have any solutions to it.

I have some tasks that must be done each week, it does not matter when I  
complete them, but they must be done before end of the week. And when the  
next week comes the task should be repeated.

Now I have an TODO item on it and I flip it back and forth from TODO to  
DONE, but it requires me to remember that I have completed the task, and  
requires me to put it back to TODO next week. This is not working very  
well.

What I would like:
At the beginning of each week the task sets itself to TODO.
When I complete it, it logs the state change (only for this state, I do  
not want state change logging on all).
A reminder that I did not complete it last week would be nice, but I  
expect that to be too much to ask for.

Does anyone use org-mode for anything like this?