Gerald's spiral to hexagonal spiral

[Creighton Dement]

Dear Seqfans, 

Sequences A108618 and A108619 plotted agains each other give what I
refer to as "Gerald's Spiral" (as mentioned in a previous post). 

Though I won't have any time to investigate this closer until sometime
next week, I wanted to share with you something I noticed a few days
ago: If Step 3 as defined for sequences 
http://www.research.att.com/projects/OEIS?Anum=A108618 and 
http://www.research.att.com/projects/OEIS?Anum=A108619

is changed from  "Step 3: Calculate x + x*y + se" to "Step 3: "Calculate
x + x*y + 2se" we get a result that does not really seem to be of any
less interest.  See half-way down: 
http://www.crowdog.de/20801/home.html

In general, the "spiral type" will slightly change each time a different
integer m is inserted into  "x + x*y + mse".   My "dream" (actually,
this is one of several!) would be to find a certain floretion-generated
integer sequence for each m, defined somehow similarly to the above,
such that, let's say, the divisors of m could be read off as "sharp
bends" in the plot when it is plotted against the natural numbers (for
example). We'll see....

Sincerely, 
Creighton