I "discovered" this theory 40 years ago (I was 16 years old). In particular, I found the formula that you attribute to Kurt Hensel in a paper by Bunjakovskiĭ published in 188... (this might be the paper "Notes about one formula related to number theory", I found it in the library of my University in Russia, it was actually the final report for a grant he received from the government of Russia, so at least the Czar cared about "digit theory"). The only outcome of my study of the "digit theory" was a problem in the Monthly and a related question in MO.
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