YearWeek calculation

I think the transformer you need is the DateTimeCalculator.

You will need to embed that in a custom transformer to create a loop construction and loop until you reach the current week.

I have created a workspace that will list the weeks.

You can download it here: weeklister.fmw

Or the python way: 

In a Python Creator and expose the attribute 'YearWeeks'

import fmeobjects
from datetime import datetime, timedelta


class FeatureCreator(object):
    def __init__(self):
        pass
    def close(self):
        startDateText = "201742" # put a start date of a week before needed
        today = datetime.now() 
        d = timedelta(weeks=1)
        endDateText = today.strftime("%Y%W")
        Currentdate = datetime.strptime("{}0".format(startDateText),"%Y%W%w")
        # had to add a weekday number to get a datetime value
        CurrentText = "0"
       
        while int(CurrentText) < int(endDateText):
            feature = fmeobjects.FMEFeature()
            Currentdate = Currentdate + d
            CurrentText =  Currentdate.strftime("%Y%W")
            feature.setAttribute("YearWeeks",CurrentText) 
            self.pyoutput(feature)

I don't like putting the week before in (201742) and also having numbers as text but datetime uses string as input and outputs. But it does work

Although excellent solutions have been provided already, it might also be a good chance to learn FME Date/Time Functions enhanced in 2017. This workflow is an example including use of some Date/Time functions (FME 2017.1+).