The Champernowne constant, C10, can easily be formed by concatenating the natural numbers to produce the real number: 0.123456789101112... etc., see e.g. here.

But this is a bit wasteful, for as young Hannah Rollman (HR) has pointed out, we can afford to * 'write down the numbers 1,2,3,... but omit any number (such as 12 or 23 or 31 ...) which has appeared as a string earlier in the sequence,'* see e.g. here.

If we concatenate the HR numbers to produce a real number we obtain: 0.12345678910111314...etc. Call this the 'HR constant'.

It is known that C10 is "10-normal". (actually it was made up specifically so as to meet that criterion) i.e. in its decimal expansion the digit 7 must appear 1/10 of the time, the string 783 must appear 1/1000 of the time, and so on.

Question: is the HR constant "10-normal"?

(Inspired by thinking about 'Loops in Pi'.)