Re: Complete the sequence problems

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sat, 17 Jul 1999, John Denker wrote:

> 1) You raise some important, indeed profound points.
>
> 2) Essentially every word that you wrote is correct in some sense.
>
> 3) OTOH there is much that is left unsaid, and it seems the big picture is
> in danger of getting lost.
>
> ...

Hi John,

You go on to (properly) criticize my 11th order polynomial as a somewhat
unappealing contender for determining the next three members of Ms. Vos
Savant's sequence.  I enjoyed your discussion of the more properly stated
problem of determining the "best extrapolation" of a sequence.

It seems to me that if one considers the set of all possible "sequence
beginnings," one will find that all but a set of measure zero will have
"best extrapolations" that have mathematical bases.  It is the rare bird
(like YYHLYEYTR perhaps) that doesn't and they are always highly
culture-dependent.

Where else but on the planet earth in the decades around the turning of
the 3rd millenium, for instance, would one find "*,0,#" a reasonable
contender for extending the sequence "1,2,3,4,5,6,7,8,9"?

And a final VERY difficult challenge for anyone: Find the "best" candidate
for the next member of the sequence EQKSIRMMDL.

John
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