How do I find the week-of-the-year/day-of-the-year?

The day of the year is in the array returned by localtime (see localtime):

    $day_of_year = (localtime(time()))[7];

or more legibly (in 5.004 or higher):

    use Time::localtime;
    $day_of_year = localtime(time())->yday;

You can find the week of the year by dividing this by 7:

    $week_of_year = int($day_of_year / 7);

Of course, this believes that weeks start at zero.