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

Sun Jan 5 21:42:46 CET 2014

A further complication is that, if I recall correctly, the sequence
contains a comment or formula giving an alternate definition: numbers which
are the sum of distinct powers of 10. This blurs the line further...

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Sun, Jan 5, 2014 at 3:36 PM, Marc LeBrun <mlb at well.com> wrote:

> Well, as Neil knows, I'll agree to respectfully disagree, and just add a
> small bit to think about:
>
>
> Proposal: if the entries are to be interpreted in different bases then this
> vital metadata really should be provided in a field (like base:2, defaultly
> understood to be 10) much like how the OEIS supports an offset: field.
>
> The current "base" keyword isn't much more than a vague warning.  A full
> base: field would  make the data more computer-friendly for things like
> transforms, as well as more user-friendly.
>
>
> Philosophy: [in case anyone else cares]
>
> Without recourse to metadata (given either informally or mathematically) it
> is NOT apparent at that the listed data values for the sequence A007088
>
>   1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101,
> 1110...
>
> "are clearly not decimal numbers".  They look like perfectly good decimal
> numbers to me!
>
> In fact the syntactic rules listed are intentionally designed to support
> decimal numbers.  More precisely, decimal numerals of a certain
> conventional
> flavor.  They are purposely crafted to rule out hex, fractions, Roman and
> strings like 00.  So why not just embrace the natural simple uniform
> semantic interpretation of the house syntax?
>
> Worse, carefully read, the description of A007088 is ambiguous and/or
> formally inconsistent.  The very first comment says "Or, numbers that are
> sums of distinct powers of 10."  So is the value listed for a(2) to be
> interpreted as two or as ten?  In binary the first prime value is a(1), but
> interpreted as sums of distinct powers of 10 it is a(2).  Which is it?
>
> Are these "numbers" really integers (the "I" in OEIS) or "strings that look
> decimal"?
>
> Given all this, what should superseeker and its ilk make of A007088?
>
> Adopting a firm foundational semantics is a key to future-proofing the
> OEIS.
>
> OK, 'nuff said.  --MLB
>
>
> >="Neil Sloane" <njasloane at gmail.com>
>
> > 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
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
>
>
>
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