base keyword usage

[Marc LeBrun]

 >=Franklin T. Adams-Watters
 > [the base keyword] should, in my opinion, mean "this is a sequence about 
how numbers are written, not about mathematics".

I'm afraid in practice the meaning of "base" has become hopelessly muddled 
and hard to change; this discussion is probably entirely moot.

So of course I'll comment (with a nod to Saint Jude)...

The keyword I'd *really* like to have is one that indicated "this sequence 
fundamentally depends on that silly decimal representation" (or "decimal 
encryption" as Bill Gosper says).  Then I could filter out most of what I 
consider irrelevant.

But that's just my taste, and tastes vary.  For example NJAS has included 
sequences like the "decimal expansion of pi", A00796.

Is that sequence "about how numbers are written", or is it "about mathematics"?

Of course base isn't just decimal, but any radix, thereby muddling things 
further.

Thus I feel obligated to check the base box whenever I submit a sequence 
that in any way involves binary expansions, though I may consider it 
perfectly serious (as opposed to, say, my "dismal arithmetic" 
contributions, although there's a serious general base-parameterized 
concept behind even those).

It might help if instead of just a keyword there was a whole field for 
specifying the base, which would be 10 for decimal, 2 for binary and so on.

But then there's "4[n]2" A065362, the "Zeckendorf expansion" A035514, the 
"Fibbinary numbers" A003714, et al where more than one base is involved, or 
exotic, or both.

Sometimes base tries to indicate that the sequence values are "in" some 
base b, but when that's the case they can always equivalently be regarded 
as ordinary values that could be expressed in rebase notation as b[a(n)]10.

Should base just indicate that some basic-expansion has something to do 
with the sequence?  If so then should it be checked for the
Moser-de Bruijn sequence A000695, because that sequence can be defined in a 
basey way--as 2[n]4--or should it not be checked since there's a non-basey 
alternative--"sums of distinct powers of 4"?

Finally, should we abuse base by further overloading or should there be 
another keyword to signal "stringy" sequences such as the cellular 
automaton A006977 or the "Look and Say" sequence A005150?

Nowadays on submission I just check it out of guilt whenever I can imagine 
someone yelling at me later for not doing so.  However I don't expect it to 
convey anything precise enough to be useful on lookups.