# [FOM] Continuous tower function

Kenny Easwaran easwaran at usc.edu
Thu Jan 17 00:53:25 EST 2013

```It looks like there has been discussion of this question on MathOverflow:

http://mathoverflow.net/questions/20688/whats-a-natural-candidate-for-an-analytic-function-that-interpolates-the-tower-f

It looks like there are several candidate answers, some of which are
complex valued, none of which has a clear claim to be the right one.  I
haven't looked through the details carefully to see how similar or
different they are though.

Kenny

On Tue, Jan 15, 2013 at 7:19 AM, Joe Shipman <JoeShipman at aol.com> wrote:

> I asked the following question here a few years ago but never got an
> that a numerical answer (precise to the nearest integer) can be obtained
> for f(3.5)?
>
>
> Let f(0)=1, f(n+1)=2^f(n).
>
> Thus f(0)=1, f(1)=2, f(2)=4, f(3)=16, f(4)=65536, etc.
>
> What is the "natural" value for f(3.5)?  (to the nearest integer if
> this is easier, but an algorithm for calculating arbitrarily close
> approximations would be preferable).
>
> -- JS
>
>
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