6=m^p-n^q?

[Brian L. Galebach]

I would submit, however, that there is a difference between conjecture and
pure speculation.
  -----Original Message-----
  From: David Wilson [mailto:davidwwilson at attbi.com]
  Sent: Tuesday, October 08, 2002 6:05 AM
  To: ZAKIRS; seqfan at ext.jussieu.fr
  Subject: Re: 6=m^p-n^q?


  You original sequence was

  10, 14, 22, 29, 31, 34, 42, 50, 52, 54, 58, 60, 62, 66, 68, 70, 72,
    76, 78, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 108, 110, 111,
    112, 114, 118, 120, 122, 124, 126, 130, 132, 134, 136, 140, 142,
    146, 150, 153, 156, 158, 160, 162, 164, 174, 176, 177, 178, 182,
    186, 188, 190, 192, 193, 194

  Besides the exclusion of 6 and inclusion of 10, this sequence contains
  several odd number and multiples of 4, all of which can be represented
  as differences of squares (someone already mentioned this).  You can
  understand how these errors throw doubt on the remaining values in
  your sequence.

  Also, there has been ample discussion to the effect that it takes some
  seriously high-powered math to show that any particular element is in
  this sequence.  In other words, the elements in the seqence you describe
  are at this point conjectural.  This is not bad thing, there are many
  conjectural sequences in the OEIS, for example, there are several
  conjectural sequences associated with the Goldbach conjecture.
  I myself submitted conjectural sequence  A023057, related to the current
  discussion.

  I know that Neil is down on adding new keywords to the database at
  this point in history, but a "conj" keyword for conjectural sequences
might
  really be useful.

  ----- Original Message -----
    From: ZAKIRS
    To: seqfan at ext.jussieu.fr
    Sent: Tuesday, October 08, 2002 1:08 AM
    Subject: 6=m^p-n^q?


    Dear All, thank you very much for the instructive discn.

    as to 6  - this is my another typo: 6 should be in the list
    (and 10 removed hence subject).

    OK, and what the number theory says now:
    can 6 be represented as difference of two full powers (not powerful
numbers) or not?
    Only imagine  these lots of fullpowers and why not differ by 6? zak

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20021008/6e226c91/attachment-0001.htm>