> Is this OBSERVATION part of a know theorem or has this OBSERVATION
> been published before? I would appreciate any references to support
> my studies.
> I would enjoy sharing my proof notes on the OBSERVATION and related
> matters with interested parties.
Yes, it has been observed before. A rather long time before, in fact.
It is a simple consequence of Rp being equal to (10^p-1)/(10-1). I
write it in this form to indicate that the result holds in all bases
when p and 10 (i.e. the base) are co-prime.