[FOM] Fractional Iteration and Rates of Growth

joeshipman@aol.com joeshipman at aol.com
Mon May 1 19:49:59 EDT 2006

Here is a much simpler version of Taranovsky's question:

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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