Can we predict the occurrence of number sequence patterns happening under RNG circumstances, that correspond not just this sequence being significant in some way, such as doubles 11,22, etc... but that the same sequence would also be occurring or the next closest sequence would be occurring, if using a different base system, rather than base 10?
Is the rate of irregularities with the number line the same, regardless of base? Do they occur at the same points in the number line? You can't get double 9's, if the base ends in 7's, for example.

So I'm looking for a way to compute these types of things across multiple base systems. And/or how the statistics of something occurring could change with numerical base changes.