Pi is an irrational number. It decimal representation does not repeat.
I strongly suspect that it does not "favor" any of the base ten digits, 0...9, nor any numbers of length when one partitions the decimal into strings of d digits. This suspicion can later be informally checked using the code below.
The following will select integers between the integers x and y, where x is less than y.
y need not have the same number digits as x. The routine will begin at the cth digit of Pi. At the end of the procedure, the counter will be at c + n.
i_/; i>x-1 && i<y+1]]
Suppose we want to generate a large (> 3000000), pseudo-random list of integers between 7 and
78. Here is how to request it. I've estimated that we'll need to use about 10^7 digits of Pi. We'll begin from position 1, that is, c=1.
(results= f[7,78,1, 10^7])//Timing
Note how the unsorted and untallied results maintain the order of Pi's digits: 314159...
Note also that the result took just under 20 seconds. As we move further along, we'll encounter practical limits to how much we can process in a reasonable amount of time. But since this is merely an exercise in thinking out of the box, we'll ignore this limitation as we proceed.
Examining the results
When we tally and plot the results we see that Pi does not particularly favor any numbers in this range:
Notice that the integers between 7 and 78 were chosen more or less with equanimity. Further tests would show this holds up.
Similar checks should show whether or not Pi plays favorites with any numbers at all, regardless of how many digits it holds. [I checked for 1, 2, and 3 digit numbers over tens of millions of draws and found no bias starting from the beginning of Pi. A rigorous check would require more systematic examination or theoretical insights.]