Regularly compiling the NumberADay blog for the MAA website has made me more aware than ever of how much we are surrounded by numbers, from street addresses and highway signs to serial numbers and other identifiers. Curious sequences of numbers may also pop up unexpectedly.

While visiting Madison, Wis., for example, I happened to notice that each bus shelter lists, in numerical order, the numbered bus routes serving that particular stop. I couldn’t help wondering whether a given list of numbers has any mathematical significance.

*Many bus lines serve this stop near the state capitol in Madison, Wis.*

*n*is in the sequence, then so are 2

*n*and 4

*n*– 1. Sloane’s entry provides information on how that particular sequence arose, along with comments, formulas, references to the literature, links to other websites, related sequences, and computer programs. You can even graph or listen to it!

Bus shelters in different parts of town are sure to show different sequences, so I’m now tempted on my next visit to Madison to collect more examples, just to see what sorts of integer sequences come up.

**References:**

*Ivars Peterson’s MathTrek*(April 8).

## 2 comments:

Your blog is soooo interesting, just found it yesterday doing some research on fractals. is good that you are there

Dear Mr. Petersen,

I have also looked at the bus numbers at bus stops in the Seattle area. But the problem here, the metro seems to change some of the numbers of buses or discontinue running them if the numbers of passengers taking a specific bus drops below a critical value. So, at least in Seattle, the bus numbers change frequently at some bus stops.

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