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<DIV><FONT face=Arial color=#0000ff size=2><SPAN class=600011513-08102002>I
would submit, however, that there is a difference between conjecture and pure
speculation.</SPAN></FONT></DIV>
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<DIV class=OutlookMessageHeader><FONT face="Times New Roman"
size=2>-----Original Message-----<BR><B>From:</B> David Wilson
[mailto:davidwwilson@attbi.com]<BR><B>Sent:</B> Tuesday, October 08, 2002 6:05
AM<BR><B>To:</B> ZAKIRS; seqfan@ext.jussieu.fr<BR><B>Subject:</B> Re:
6=m^p-n^q?<BR><BR></FONT></DIV>
<DIV><FONT face=Arial size=2>You original sequence was</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>10, 14, 22, 29, 31, 34, 42, 50, 52, 54, 58, 60, 62, 66, 68, 70, 72,
<BR> 76, 78, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 108, 110, 111,
<BR> 112, 114, 118, 120, 122, 124, 126, 130, 132, 134, 136, 140, 142,
<BR> 146, 150, 153, 156, 158, 160, 162, 164, 174, 176, 177, 178, 182,
<BR> 186, 188, 190, 192, 193, 194<BR></DIV>
<DIV><FONT face=Arial size=2>Besides the exclusion of 6 and inclusion of 10,
this sequence contains</FONT></DIV>
<DIV><FONT face=Arial size=2>several odd number and multiples of 4, all of
which can be represented</FONT></DIV>
<DIV><FONT face=Arial size=2>as differences of squares (someone already
mentioned this). You can</FONT></DIV>
<DIV><FONT face=Arial size=2>understand how these errors throw doubt on the
remaining values in</FONT></DIV>
<DIV><FONT face=Arial size=2>your sequence.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Also, there has been ample discussion to the
effect that it takes some</FONT></DIV>
<DIV><FONT face=Arial size=2>seriously high-powered math to show that any
particular element </FONT><FONT face=Arial size=2>is in</FONT></DIV>
<DIV><FONT face=Arial size=2>this sequence. In other words, the elements
in the seqence you describe</FONT></DIV>
<DIV><FONT face=Arial size=2>are at this point conjectural. This is not
bad thing, there are many</FONT></DIV>
<DIV><FONT face=Arial size=2>conjectural sequences in the OEIS, for example,
there are several</FONT></DIV>
<DIV><FONT face=Arial size=2>conjectural sequences associated with the
Goldbach conjecture.</FONT></DIV>
<DIV><FONT face=Arial size=2>I myself submitted conjectural sequence
A023057, related to the current</FONT></DIV>
<DIV><FONT face=Arial size=2>discussion.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I know that Neil is down on adding new keywords
to the database at</FONT></DIV>
<DIV><FONT face=Arial size=2>this point in history, but a "conj" keyword for
conjectural sequences might</FONT></DIV>
<DIV><FONT face=Arial size=2>really be useful.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>----- Original Message ----- </DIV>
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style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=zfseidov@ycariel.yosh.ac.il
href="mailto:zfseidov@ycariel.yosh.ac.il">ZAKIRS</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=seqfan@ext.jussieu.fr
href="mailto:seqfan@ext.jussieu.fr">seqfan@ext.jussieu.fr</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, October 08, 2002 1:08
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> 6=m^p-n^q?</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002>Dear All, thank you very much for
the instructive discn.</SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002></SPAN></FONT> </DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN class=200403604-08102002>as
to 6 - this is my another typo: 6 should be in the list
</SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002>(and 10 removed hence subject).</SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002></SPAN></FONT> </DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002>OK, and what the number theory says
now:</SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002>can 6 be represented as difference of two full
powers (not powerful numbers) </SPAN></FONT><FONT face=Arial color=#0000ff
size=2><SPAN class=200403604-08102002>or not? </SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2><SPAN
class=200403604-08102002>Only imagine these lots of fullpowers
and why not differ by 6? zak</SPAN></FONT></DIV>
<DIV><FONT face=Arial color=#0000ff
size=2></FONT> </DIV></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>