As others stated, this information was readily available in the book, The Art of Patrick Nagel, and was also listed on Mirage's price sheets, which most galleries selling Nagels back in the 1980s updated in the Mirage Editions three ring binder catalogs that I always saw when I visted the various galleries around town.
Those price sheets have been posted and cross-referencing them against the information in the book provices a pretty clear idea of the all the various proofs, doubles and so on. In 35 years of collecting, tracking auctions, and collborating with peers from the previousl forum, I have never seen an AP of a special proof. I have SPs of "Mirage" "Just Looking" and the "State 1" versions of "Papillon." It does not make sense that there would be an AP of an SP.
All the ones I have seen are marked SP or "State 1." I think it is best to keep identifying them as "special proofs," which is how Mirage identified them.
Do you have a copy of the book? I ask because I keep seeing comments that checking the book and verifying against the price sheets would answer, even with the book's errors and omissions regarding issues like the omission of "Shades" having a signed in screen state and some of the doubles, and some images mis-identified or flipped.
Here is part of Nagelite's post (which is a copy of my text) to this forum in April of 2009:
PRINT TYPE: Serigraph (aka "Silk-Screened Print" on 100% archival grade rag.)
RELEASED BY: Mirage Editions, Inc.
PRINTED BY: Samper Silkscreen
RELEASE DATE: September 1981
-HAND SIGNED AND NUMBERED: 250
-ARTIST'S PROOFS (SIGNED): 40
-SIGNED IN SCREEN (UNSIGNED): 1200
-SPECIAL PROOFS (SIGNED): 40
DIMENSIONS: 17" x 25 3/8"
OTHER VERSIONS RELEASED?: Yes, aside from the special proofs, which are hand signed by Pat and marked "S/P," this image, which was immensely popular was re-released as 24" x 36" unlimited edition lithograph poster in order to promote the soft cover release of The Art of Patrick Nagel.
The "Special Proof" version omitted the text "MIRAGE" running down the upper right hand corner of the print.
Just a note to everyone who is collecting:
As I continue to interview players in the Patrick Nagel story, one aspect that has come to light should interest all you serious collectors. There are several lifetime, signed serigraphs that were issued both with and without commercial deisgnations. For example, "Mirage" was issued with the vertical spelling of Mirage along the right side of the image. A very limited number of that issue were printed without the designation. Those serigraphs printed without designations, I'm told, are considered more highly valuable than the printed variety. They are often A/P and S/Ps.