A121760/1: two (interesting?) sequences

[cino hilliard]

Re:"To base or not to base. That is the question"

Hi Jonathan,

Good exposition on the human equation and quantification of the base 
sequences in your . To me,
the key word "base" is vague. when I think of the word base in mathematical 
terms I think of some
sort of conversion where you transform a number from one base to another.  
For example,
using my Pari specific base converter base(b1,b2,text)

http://groups.msn.com/PariUtilitiesandscripts/baseconversion.msnw

the sequence 1,7,2,3,4,1,0,4,1,7,2,4,2,8,6,9,8,3,4,4,9,5 is an interesting  
base sequence.
Try base(10,91,1723410417242869834495) and you will find it is, indeed, 
interesting.

It is base because  we are going from base 10 to base 91 for the result. 
However, when base 10
is implicit and we fumble with the digits to invent something, I do not see 
how that is base.

>>But what is, for example? Everything in combinatorics, count on it,
>>will appear sooner or later in other fields like physics, IT, biology and 
>>more,

If this means every sequence in combinatorics, then I wished I knew how to 
say it in
Spanish. "When a snake walks on its hind two legs, then "Every sequence in 
combinatorics will
appear sooner or later in other fields like physics, IT, biology and more"

Consider A010888  Digital root of n (repeatedly add digits until reach a 
single digit).
Here we are staying in base 10. I do not see why this as a base sequence. If 
we had a
sequence  Digital root of n base 10 in  base 16  (repeatedly add digits 
until a single digit is reached
base 16), I would define it as base. Eg., base10 1000 = 3E8 base16. So Hex 
3+E+8 = 19, 1+9 = A.
(note the def of A010888 needs to be edited)

Another example is A016051. Why is this "numbers of the form" sequence a 
base sequence while
another "numbers of the form" A003586  not a base seq.?

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?

While I know the OEIS is not a Democracy, I vote the vague, and repugnant  
key word: base be
removed from the database. :-)

my 10 1/64,
Cino