Blue Jays Moving

All day today I've noticed blue jays migrating. Some are carrying an acorn in their bills as they fly. Is this food for the trip? I wonder...
When it's autumn and the small flocks of jays are moving over Indigo Hill, our southeastern Ohio farm, we scan them for red-headed woodpeckers. The red-headed woodpecker (one of my favorite birds) is another acorn specialist that seems to migrate at the same time as the blue jay. I wish the 37 jays I've seen so far today had been red-headed woodpeckers.