I think I know what you are trying to do, but dont think it is as easy as we would like. Common sense would suggest that if you have 39 frames in a comp and use that comp as a texture source for Particular, it would cycle through and use each frame until it starts using duplicate frames. Unfortunately, that is not the case. The only way I know of to control the frames is to use the new texture based on frame capability of particular. Set your particles per second to the frame rate of your comp and have particular emit until frame 39. This will emit one particle per frame and only emit 39 particles, each with a different texture from the source texture comp. I hope this makes sense.
Just the obvious one...make sure you dont have the pps keyframed to 0 at that frame. The time sampling I was recommending was "Current Frame - Freeze" which will emit particles textured with the layer you choose on that frame and hold that texture. It is the only way I know of to specifically control the order of the particles and not have them change.