Since I'm in an inventive mood, let's see what my brain can patch together.
Ok, so we know there are about 7 days in a week, yes? And if there are 42 weeks gone by, there are 42*7 days (294)
So we've established the day of the year *but* it will be the same day as the start of the year, since we haven't done anything about the first day of the week or whatnot.
Now this is a disgusting little piece of code that will make your insides curl up and wiggle, but when I tried it out it accepted the "month=1", "day=294" and spat out the 20th of October, later confirmed as the 293rd day of the year. Hey, it's close enough.
Now we have wednesday the 20th of October, we need to sort out the first day of the week. Using date("w") will tell you that Wednesday is the 3rd day of the week (with Sunday as 0)
So now we can do the mktime function again, reducing the days by 3 to get the sunday of that week.
Sun Oct 17, 2004.
date("W") = 42nd week of the year.
Am I good or what?