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.

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

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