Sequences in Higher Bases

[Antti Karttunen]

> Christopher Tomaszewski wrote:
> 
> Fellow SeqFan Members,
>     I was wondering why Neil doesn't allow letters to be used in submitting sequences so as to facilitate the submission of sequences that are composed partially or entirely of terms in bases higher than ten, namely hexadecimal. Since this will reach Neil, perhaps he
> can reply personally.

There's at least one really hexadecimal sequence accepted into OEIS,
namely: http://www.research.att.com/projects/OEIS?Anum=A048708
(I'm to blame.)

Seriously, I think many consider there are already enough base-10
sequences in OEIS, and working with any higher arbitrary bases
would just multiply the amount. Of course, certain bases
like binary, ternary, quaternary have their elegant uses,
but I think much more unfound mathematical gems are waiting to
be found if you switch to Zeckendorf-expansion (i.e. "Fibonacci number system),
see:

     http://www.research.att.com/projects/OEIS?Anum=A003714
  or http://www.research.att.com/projects/OEIS?Anum=A014417

or to factorial expansion,

  see http://www.research.att.com/projects/OEIS?Anum=A007623

see also its variant at:
  http://www.research.att.com/projects/OEIS?Anum=A072001

The Fibonacci number system has connections to such beatiful things
as Wythoff-array:
  http://www.research.att.com/projects/OEIS?Anum=A035513

and the factorial expansion has interesting uses when
one generates permutations by any of the usual unranking
algorithms.



Terveisin,

Antti Karttunen