[seqfan] Re: A090709 Decimal primes whose decimal representation in base 6 is also prime. -- rebasing

[Neil Sloane]

I don't quite agree with everything Marc LeBrun said.

Look at http://oeis.org/A007088, the binary numbers.
These are written in base 2. They are clearly
not decimal numbers.

What is true is that numbers in the DATA lines in
the OEIS are written using the digits 0 through 9
(and, apart from 0 itself, may not begin with 0).
But it is misleading to call such numbers "decimal numbers".

Of course there are other rules too: no "decimal" point,
no internal commas or spaces or periods, minus signs are allowed but not
plus signs, etc.

Neil


On Sun, Jan 5, 2014 at 1:10 PM, Marc LeBrun <mlb at well.com> wrote:

> >="Veikko Pohjola" <veikko at nordem.fi>
> > Should there be some unification of the terminology?
>
> Yes, and here's a possible starting point:
>
> Once upon a time we discussed canonizing the idea of "rebasing" which
> covers
> many of these situations.
>
> The definition of "rebasing n from a to b" is roughly "expand n in powers
> of
> a, then replace a with b".
>
> Thus A090709 might be described succinctly as "primes that when rebased
> from
> 10 to 6 are prime".
>
> A major benefit of adopting and using this concept is that it clarifies
> that
> ALL sequences in the OEIS are ALWAYS sequences of INTEGER values that are
> ALWAY written in DECIMAL.
>
> In particular it establishes that the values are never in any other base,
> nor are they digit strings or other flavors of non-numerical objects.
>
> After all, it's the "On-line Encyclopedia of INTEGER Sequences".  And it's
> customary for integers to be "written in decimal" (that redundancy,
> repeated
> in 400+ entries, flags that *some* clarification might be in order!<;-).
>
> Rebasing has many other pleasant ramifications in addition to eliminating
> lots of awkward, inconsistent, imprecise and ambiguous circumlocutions.
>
> For instance in defining a transform it relieves concerns about what base
> to
> use to interpret the input values.
>
> Admittedly it takes a little getting used to the idea that, for example,
> the
> concise definition of A007088 is "numbers rebased from 2 to 10", but I
> think
> the advantages in increased precision are well worth it.
>
> A side-benefit is that rebasing is an operation with widespread interesting
> and useful applications.  For example rebasing from 10 to 1 sums the
> digits,
> and rebasing from 10 to -10 reverses them (mod a left-shift).
>
> More generally it encourages a standardized viewpoint for expanding
> integers
> into polynomials and evaluating polynomials back into integers at a base.
>
> For example rebasing A014580 from 2 to 10 gives A058943.  Rebasing to X
> gives the actual polynomials, which never appear directly in the OEIS, but
> are perfectly reasonable in definitions or computations with numerical I/O.
>
> And so on...
>
> Anyway, back in the day I was writing, say 10[n]6, to mean "rebase n from
> 10
> to 6" from a psychedelic analogy with notations like GF2[n](X).  Franklin
> T.
> Adams-Watters proposed n_10->6 which is more suggestive.  Ultimately the
> notation discussion trailed off inconclusively; there are now entries with
> a
> diversity of notations, conventions and terminology.
>
> Yes, this should all be unified.
>
> --MLB
>
>
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com