[seqfan] Is the pi power tower beyond our reach?

[Alonso Del Arte]

A question that recently came up on Math.StackExchange: "Why is it so
difficult to determine whether pi^(pi^(pi^pi))) is an integer?"

Our own Charles answered: "That number has 666262452970848509 decimal
places, so to determine if it's an integer you'd have to compute it with
that precision. But this would take 270,000 TB, and we don't have many hard
drives that large."

In the OEIS we do have A073234, which is the decimal expansion of
pi^(pi^pi). But we don't seem to have the decimal expansion of
pi^(pi^(pi^pi))). Even Google can give a decent approximation to pi^(pi^pi)
in scientific notation, but draws a blank if you take the tower up one
level.

As an aside, I posted what (at the time) I thought would be an easier
problem: to determine if (22/7)^((22/7)^((22/7)^(22/7))) comes even close
to being an integer. My instinct is that it is not, and neither is
pi^(pi^(pi^pi))).

Al

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Alonso del Arte
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