In reply to albert_ross:
Jays are beautiful. Too often, all I see is their white rump as they fly away. Seen side on, or from above they are fantastic birds. Jays are also some of the most intelligent birds of all. There was a fascinating article in New Scientist a year or two ago, showing that some species of jay appear to be able to think ahead and make allowances for what they would do in another bird's place. (e.g. A jay who is hiding food may return and move it to another hiding place if he notices that he is being watched as he hides it.)
I've seen jays and green woodpeckers in the same area, but not interacting. I once saw a greater spotted woodpecker and a green woodpecker flying from the same patch of woodland almost as if they were together.
Greater spotted woodpeckers tend to bully smaller or less aggressive birds, and defend their food supply quite vigorously.