#Pyth, 25 bytes
Pyth, 25 bytes
M?H.UgbtH*G]3^3Gug3tG64 4 The first part M?H.UgbtH*G]3^3G defines a method g(G,H) = u(3,G,H+1).
To test the first part, check that 7625597484987=u(3,3,2)=g(3,1): g3 1.
The second part ug3tG64 4 starts from r0 = 4 and then compute rn = u(3,3,r(n-1)) = g(3,r(n-1)) 64 times, outputting the final value (r is chosen instead of g to avoid confusion).
To test this part, start from r0=2 and then compute r1: ug3tG1 2.