The N53 between Dundalk and Castleblayney strays across the Northern Irish/Republic of Ireland border for just over 3 miles to pass through Cullaville. In Northern Ireland the road is numbered A37.
Approaching the crossroads in the centre of Cullaville
It has been speculated that the existence of the duplicate A37 may be an mis-transcription of the A97 number, which is otherwise unused in Northern Ireland but appears in this location in 1940s Bartholomews mapping. This was debunked when the original road lists were found, showing this to be the oldest duplicate A-road in existence (there are also two duplicate B-roads in Northern Ireland dating to the original classification).
N53 to A37 youtube video