xy+yz+zx

[Richard Guy]

Many thanks to several respondents.  The only addition
might be the reference

Mao Hua-Le, Publ Math Debrecen, 52(1998) 159--165;
MR 98j:11016.              R.

On Thu, 14 Jun 2001, Olivier Gerard wrote:

> 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.
> > 
> > 
>