This is not answered in the previous related questions I've seen/read - AFAICT.
I always login at Stack Overflow. Since I joined up, I've had the habit of typing "Stack" into Google and clicking the top result (or second, depending on how many links the magazine has been throwing around).
I then login through SO, and navigate from there to MSO, MSE, etc.
Yesterday/day before, I had about 56 consecutive on SO, and lower on other sites, however currently I have:
SO - 3 consecutive
MSO - 13 consecutive
MSE - 13 consecutive
Not sure where the consecutive have gone from SO, but also, as I always login in at SO first, how could that be lower than the others?