--- In

primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:

>

> Ronald Dwyer wrote:

> >> Using a run sum calculator website, I found the numbers in the range

> >> 1 to 150 (this was arbitrary) that are the sums of exactly 2 runs.

>

> Mark Underwood wrote:

> > From a cursory glance at the numbers Ronald has provided, this seems

> > very remarkable to me.

>

> Maybe you didn't receive my post which explains it:

> http://tech.groups.yahoo.com/group/primenumbers/message/19444

> The key is that a runsum can be written as a product (where one of

> the terms may be 1).

>

> > when I add two run sums together I get a number not on Ron's list:

> >

> > (2+3+4) + (6+7+8+9) = 39.

>

> Ronald meant numbers for which there are exactly two different runs

> with the same sum, for example:

> 41 = 41 (the sum of one number), and 41 = 20+21 (the sum of two numbers).

> All odd numbers have these two sums. There are more sums if and

> only if the number is composite, for example 39 = 12+13+14 = 4+5+6+7+8+9.

>

> --

> Jens Kruse Andersen

>

OK I get it now, he said sheepishly. I find it amazing the lengths I can go to misunderstand

a problem! :)

Thanks Jens.

Mark