MathDB

f_0(x) = x, f_{2k+1} (x) = 3^{f_{2k}(x)}, $f_{2k+2} = 2^{f_{2k+1}(x)}

Source: Austrian Polish 1989 APMC

April 30, 2020

recurrence relationfunctionalgebra

Problem Statement

Functions

f_0, f_1,f_2,...

are recursively defined by

f_0(x) = x

and

f_{2k+1} (x) = 3^{f_{2k}(x)}

and

f_{2k+2} = 2^{f_{2k+1}(x)}

k = 0,1,2,...

for all

x \in R

. Find the greater one of the numbers

f_{10}(1)

and

f_9(2)