This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Title: Cliff Puzzle 5: Mystery Sequence
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Thanks, Cliff Pickover
* * *
What is the next term in the Mystery Sequence:
22.45906, 17600.22, 0.34714E+12,
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.
In article <+M_UUYZ8email@example.com> you write:
>firstname.lastname@example.org (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 email@example.com Fermilab
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 firstname.lastname@example.org Fermilab
BS 1978 Applied Math & Physics; PhD 1985 Physics
Before I go barking up a wrong tree, I notice that
e Pi = 22.45916
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