U.S. 312
With US 112, I already provided a link between US 12 and US 412, but then I thought, "Why not add a second connection between the two highways?"  And this is where US 312 comes into play. US 312 starts at Lemmon, SD, well short of the North Dakota line.  It replaces all of SD 73, NE 61 and KS 161.  After a multiplex with US 36, it heads south on KS 27 from Wheeler to Elkhart.  In Oklahoma, it replaces OK 95 to Eva.  After turning east on US 412, it then turns south on OK 136 at Guymon and follows TX 136 all the way to Amarillo, where US 312 would end at an intersection with US 60.