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[Jonathan Sondow]

You're correct, 9 is wrong. You're also correct, I
believe, about the sequence in general. It makes sense
-- consider that for F_2, there are two possible root
sequences:

1 3 5 7 etc.
2 4 6 8 etc.

For F_3, three:

1 4 7 10
2 5 8 11
3 6 9 12

And so on. There will be exactly one representation
for each of those root sequences, and the
multiplicative form of the numbers with those
representations will be:

3*2 = 6
5*5 = 25
5*6 = 30
7*10 = 70
7*11 = 77
7*12 = 84
9*17 = 153
9*18 = 162
9*19 = 171
9*20 = 180
11*26 = 286
11*27 = 297
etc.

Thanks to David and Max for your help!

    -Andrew Plewe-



--- Max Alekseyev <maxale at gmail.com> wrote:

> On Sun, Mar 30, 2008 at 10:59 PM, Andrew Plewe
> <aplewe at sbcglobal.net> wrote:
> > I'm re-evaluating the sequence you
> > came up with; so far I've verified these values up
> to and including 30:
> >
> >  6,9,25,30
> 
> Why 9 is here?
> 
> Except for that number, this sequence seems to be
> the numbers of the
> form a*(2*r+1) where r^2 < a <= r*(r+1).
> 
> r=1: a=2  ~ 6
> r=2: a=5  ~ 25
> r=2: a=6  ~ 30
> r=3: a=10 ~ 70
> r=3: a=11 ~ 77
> r=3: a=12 ~ 84
> ...
> 
> Regards,
> Max
>