Does the number
$$3\uparrow \uparrow 4 = 3^{3^{3^3}}$$
contain the digits 0-9 approximately equally often ?
With "approximately" I mean that a chi-squared test for equal distribution would produce no value greater than 17 (about the critical value at the 5%-level).
Is it necessary to calculate the number to find that out, or is there a better way ?
It is relatively easy to calculate the last digits of such big numbers, but is there a method also for the first ones ?