[SeqFan] On the base nature of base.

[Antti Karttunen]

cino hilliard wrote:

>
> Here is another one..
> A014486
> List of totally balanced sequences of 2n binary digits written in base 
> 10. Binary expansion of each term contains n 0's and n 1's, and 
> reading from left to right (the most significant to the least 
> significant bit), the number of 0's never exceeds the number of 1's.
>
> Why isn't this a  base sequence?
>
Probably because it didn't contain "base" when originally submitted by 
Wouter Meeussen,
or because I subsequently removed it when I edited the entry.
So far I have left the "base" out from the sequences that are based
on some constraint on the binary, Fibonacci or factorial expansion of n,
but are themselves represented in the normal OEIS way (entries to be read
as _decimal_ numbers). However, the corresponding sequence showing
the same terms in the base where the constraint is used, should off course
contain "base." So for A014486, A063171 is the corresponding "base" 
sequence,
and for A003714, from which I edited "base" out in February AND added this
note to Neil:

  FURTHERMORE, I have removed the "base" keyword, on the same grounds
  that most of the other decimal representations of
  2-automatic/2-regular sequences in OEIS don't contain it. As like this 
one,
  they often have simple recursive formulae, and may pop up as answers
  to some interesting "non-basal" number theoretical questions, like
  those binomial identities given by Benoit Cloitre.
  (Please put it back if you disagree....)

The corresponding "base" sequence of A003714 is A014417. (The first one 
on Jonathan Post's list, btw.)

Yes, I understand the rationale if sequences like A014486 and A003714
should be tagged "base" as well. On the other hand, the other extreme would
be that the sequences like A000079 (the binary expansion contains a 
single 1!) and
A000668 (Mersenne primes, but also: "Prime repunits in base 2.")
should be tagged as "base". The problem here is that most people (so I 
think)
use the keyword "base"  in searches much more for exclusion than 
inclusion. ("-keyword: base")

But I will wait the decision of the final arbiter (njas) on this subject.

Moreover, I think that on the whole the keyword-system of OEIS should be 
made
more exact and extensive. E.g. any "hardcore combinatorial" sequence
that is known to count some structures should contain keyword like "enum"
or "count", permutations of integers keyword "perm", and so on.
That way the serious users of the database wouldn't need to bother
so much with all the "base" and "avant-garde" experimentations
of us the tinkerers.


Yours,

Antti Karttunen