Consecutive routes

Pittsfield has US-7, MA-8, and MA-9 (and there are signs from US-20 that list all three).  Routes 7 and 8 don't connect.  But, if you're on MA-8, then you can go east to MA-9, and when you get to Northampton, you can turn on to MA-10.  If you go north a very long way, staying on Route 10, then NH-10 intersects NH-11 in Newport, NH; go west and you'll reach NH-12 before you cross the Connecticut River; go back south into Massachusetts and MA-12 will reach MA-13 in Leominster.

So: what is the longest chain of consecutively-numbered routes you can connect?  You can cross a state line, but only if the road keeps the same number (NY-7 turning into VT-9 breaks the chain).  No specific need to start with Route 1.  No subsidiary routes (MA-2A, "business" routes, &c.; 3-digit routes like I-290 or US-202 are legitimate but have to stay in sequence).  Distance doesn't matter (starting in Key West, taking US-1 to US-2 in Maine, then to US-3 and US-4 in New Hampshire and then US-5 in Vermont is a legitimate start) (but if you start off this way, US-7 runs parallel to CT/MA/VT-8 and does not intersect anywhere).