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

[Jack Brennen]

It's there...  Pi^(Pi^(Pi^Pi)).

http://oeis.org/A202955



On 7/2/2014 10:13 AM, Alonso Del Arte wrote:
> 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
>