Title: Cliff Puzzle 5: Mystery Sequence From: cliff@watson.ibm.com
pickover/pickover.05
Problem
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,
Show solution
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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
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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
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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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