With the help of interactivetools.com, we set up a system for a client that I referred to as "Routed Emails". It was really a chain of emails that went into effect on a key date, in this case the date that that member started their membership.
ie. on Day 1, we send the "Welcome email", Day 3 the "Introduction to the team", Day 5 the "Let us now how you like the system"..... Day 364 "Your account expires tomorrow".
We had a number of these Routed emails, each with different "rules" such as membership groups, status, last log-in date etc.
Included in each email template was the ability to include custom placeholder content - and I think this is key to you're requirement, and in your case would be a list viewer of articles since today - 30days. The key date would be every Tuesday...
So yes - certainly possible, but a bit of thought needs to go into it and how you may want it to grow over time. IT could build it for you.
Cheers,
Tim (toledoh.com.au)