[seqfan] Re: Why does this sequence make a staircase pattern?

[Hans Havermann]

EB: "How did you find it? And could you please compute some more terms?"

I've shared my Mathematica code with Elijah. I'm currently approaching 10^9 in my record-length "order" search and a log graph nicely illustrates the "staircase":

http://chesswanks.com/num/EB'sOrderStaircase.png

"... why could these 'plateaus' and 'cliffs' occur?"

Each number represents a record-length sequence so it shouldn't be too surprising that we might have to climb some distance to find a new one. The sequences themselves have the characteristic, often, of being extendable by prepending another number. Sometimes, when we are in new territory, this can be done many times. In the plateaus, we extend our records by exhausting this feature in the nearby integer terrain.