xy+yz+zx

[Olivier Gerard]

Dear Richard,

this sequence was added by Clark Kimberling a while ago
and already corrected by Ron Harding (bell labs)
under the ref:   A025052

References in this entry will lead you to other lists
of numbers non representable by various other forms.


%I A025052
%S A025052 1,2,4,6,10,18,22,30,42,58,70,78,102,130,190,210,330,462
%N A025052 Numbers not of form ab + bc + ca for 1<=a<=b<=c (probably the list is complete).
%D A025052 J. Borwein and K.-K. S. Choi, On the representations of xy+yz+zx, Experimental Math., 9 (2000), 153-158. [Jonathan Borwein (jborwein at cecm.sfu.ca), choi at cecm.sfu.ca (Stephen Choi)]
%H A025052 <a href="http://www.cecm.sfu.ca/ftp/pub/CECM/Preprints/Dvi/98:119-Borwein-Choi.dvi">Borwein-Choi paper (dvi)</a>
%H A025052 <a href="http://www.cecm.sfu.ca/ftp/pub/CECM/Preprints/Postscript/98:119-Borwein-Choi.ps.gz">Borwein-Choi paper (ps)</a>
%Y A025052 Cf. A027563, A027564, A027565, A027566, A055745, A034168.
%K A025052 nonn,fini,nice
%O A025052 1,2
%A A025052 Clark Kimberling (ck6 at cedar.evansville.edu)
%E A025052 Corrected by Ron Hardin (rhh at research.bell-labs.com)

About the fact that some sequences in the EIS are finite, while this is not
the essence of the EIS, there are currently 2033 sequences known to be finite,
of which 1387 are in full in the database.

regards,

Olivier

On Thu, Jun 14, 2001 at 08:51:05AM -0600, Richard Guy wrote:
> I believe that Neil occasionally breaks his rule
> that sequences should be infinite.  I expect
> that the discriminants of complex quadratic
> fields with class number one are there, and
> perhaps the notorious example of which one
> member is `Columbia University'.  I don't know
> if the following is there.  If not, could
> some Seqfan or Munster find the details and
> offer them to Neil?
> 
> >From MR 2001e:11033 I learn that J Borwein &
> S. Choi (and before them Mao Hua-Le) have
> shown that there are 18 numbers not
> representable as  yz + zx + xy  with x y z
> positive integers, and, failing GRH, a 19th
> larger than 10^{11}.
> 
> A hasty & no doubt erroneous guess at the first
> few members is
> 
> 1  2  4  6 10 18 22 30 42 58 ...     R.
> 
>