Most links in a chain of intersecting highways with consecutive numbers?

[KCRoadFan]

Here's something I thought of a little while ago. Imagine you're driving down a highway, and you see another road that intersects it, with a number one greater than that of the highway you're on. You turn off onto that other road and eventually come across another highway with the next higher number, which in turn intersects yet another road with the following consecutive number - thus creating a chain of highways with multiple numbers in sequential order, where each highway intersects the next one in turn, making the sequence such that it could conceivably be driven in one trip, without using any other highways in between. I wonder what the chain with the most such links might be - here's a great example of that phenomenon that I've found:

• US 34 intersects I-35 in Osceola, IA
• I-35 intersects US 36 in Cameron, MO
• US 36 intersects IN 37 in Indianapolis, IN
• IN 37 intersects IN 38 in Noblesville, IN, just northeast of Indy
• IN 38 intersects IN 39 just south of Frankfort, IN
• IN 39 intersects US 40 in Belleville, IN, west of Plainfield
• US 40 intersects US 41 in Terre Haute, IN

Incidentally, for what it's worth, IN 42 also comes close to Terre Haute - if it went a few miles further west, it would continue the chain. Where throughout the country might some other such long chains of consecutive intersecting highways be found, and how many links do they have?

As you can see in my example, for the purposes of this fun little exercise, Interstates, US highways, and state highways can all be used. Each highway link must intersect both the previous and next one in the list, and interstate and US highways can cross as many state lines as they need to in order to find a highway of the next consecutive number. In addition, state highways that retain the same number across state lines can also be used as a multi-state link if need be. (For example, VT 9 becomes NH 9; for the purposes of this exercise, VT 8 > VT 9/NH 9 > NH 10 is a valid chain.)

I can't wait to see what people can come up with here! This should be fun.

[hotdogPi]

Tying the OP: US 1-2-3-4-5-6-7. US 7 parallels CT/MA/VT 8 but unfortunately doesn't touch it.

(Although there's no ramp from US 5 south to US 6 west – not sure if that disqualifies it.)

That said, US 6 goes across the country; maybe it can continue the chain in an entirely different state?