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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

381 pickover/pickover.05.p


Title: Cliff Puzzle 5: Mystery Sequence
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
address, affiliation, e-mail address. If you like, tell me a little bit
about yourself so I can cite you appropriately if you provide unique
information. PLEASE ALSO directly mail me a copy of your response in
addition to any responding you do in the newsgroup. I will assume it is
OK to describe your answer in any article or publication I may write in
the future, with attribution to you, unless you state otherwise.
Thanks, Cliff Pickover

* * *

What is the next term in the Mystery Sequence:

22.45906, 17600.22, 0.34714E+12,

pickover/pickover.05.s

-------------------------

Some serious roundoff error going on here, but...

The sequence 22.45906, 17600.22, 0.34714E+22 is clearly meant to be:

Pi^e, (Pi^e)^Pi, ((Pi^e)^Pi)^e,

so the next term should be (((Pi^e)^pi)^e)^pi = 1.80169E36.

Actually, it looks like you were using "pi" = 3.14159 and "e" = 2.71828, possibl
with other intermediate rounding off, so you may have been looking for something
more like 1.8011E36.

James
jlayland@grissom.jpl.nasa.gov
-------------------------

In article <+M_UUYZ8!@linac.fnal.gov> you write:
>cliff@watson.ibm.com (cliff) writes:
>>What is the next term in the Mystery Sequence:
>>
>>22.45906, 17600.22, 0.34714E+12,
>
>I disagree about the last couple of significant digits, but otherwise
>the series is pi^e, (pi^e)^pi, ((pi^e)^pi)^e, ... and the next term
>is about 1.8017E+36.
>_________________________________________________________
>Matt Crawford crawdad@fncent.fnal.gov Fermilab
>
>

Background:

I recognized the approximate value of the first term from figuring
out (during high school, about 20 years ago) the old question of
which is larger, e^pi or pi^e. After that it was a mater of taking
ratios of logs of the terms.

_________________________________________________________
Matt Crawford crawdad@fncent.fnal.gov Fermilab
BS 1978 Applied Math & Physics; PhD 1985 Physics
-------------------------

Before I go barking up a wrong tree, I notice that

     e
   Pi   = 22.45916

>22.45906, 17600.22, 0.34714E+12,
which seems suspiciously close to your first constant. Which should I assume?

"Typo. It should read 22.45916",
"Coincidence.",
or "No Comment -- no clues."

???

/Alan Paeth
-------------------------

In article <1992Sep17.132745.21035@watson.ibm.com> you write:
>What is the next term in the Mystery Sequence:
>22.45906, 17600.22, 0.34714E+12,

As a one-time math major, I thought I recognized that telltale 22.45906 ...

The sequence continues with 1.8016851E+36

Steve
--
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