[seqfan] Re: Arithmetic progressions such that adjacent terms have a common non-zero digit
Benoît Jubin
benoit.jubin at gmail.com
Tue May 28 18:03:16 CEST 2019
>
> I think we agreed that terms with trailing 0 should be excluded, since
> these are trivial solutions.
>
Why should trivial solutions be excluded by principle (not only for this
sequence, but in general)? I think that if one wants a sequence of
"nontrivial solutions", this should be a second auxiliary sequence.
> > > - A positive integer n has this property if and only if 10*n has
> this
> > > property.
>
> I disagree with the last one, since for ANY integer n > 0, 10n has the
> required property.
>
You may have overlooked the requirement that multiples share a *nonzero*
digit.
By the way, which digit it is (or which they are) could also be
interesting. It looks like it will most often be 9.
As with my previous intervention here, and as often with "base" sequences,
looking at the situation in smaller bases could be interesting (here base 2
is trivial, but already base 3 can be interesting).
Benoît
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