Just digging into protection of stairs, when NFPA 13 2013 edition calls out protection under the first "accessible" landing, is this underneath the 2nd floor landing as you look up?
I believe it is in reference to the first intermediate landing (i.e, where stuff could potentially be stored under).
13-13 8.15.3.2.3.1 seems to confirm this, by saying that if the space under the stairs is blocked off so that storage can't occur then you don't need any sprinklers at the bottom.
There are many who still think it is above the door for egress. That is incorrect. To clarify, the required sprinkler will be around 5'-0" AFF depending on construction type.
Just an aside, be aware of the difference between a stair and a stairwell.
We recently had an AHJ ask us to install sprinklers beneath every landing in a stairwell. NFPA 13 has a distinction between stairs and stairwells. Thankfully it was clearly worded enough to distinguish.