Straps of newer consecutive serial numbers seem to draw a premium from buyers looking to pluck out "fancy" serial numbers. So one strap may sell for a good deal more than the next simply because of the serial number range. What makes this particularly unpredictable is the loose definition of "fancy".
With older or rarer notes sellers always try to get a premium for even two graded consecutive serial numbers together. But I don't know how often they obtain it. Sure having two consecutive notes is a rarer thing but that doubles the cost of ownership which limits the number buyers. When it comes to the old and the rare I think most would rather have two different things instead of consecutive serial numbers.
For common notes, even some older notes like SC's there is no premium for consecutive serial numbers and in fact consecutive numbers is more or less buying/selling in bulk and becomes cheaper than what you might pay if you bought the notes individually.