[seqfan] Re: How many numbers have n letters?

[Allan Wechsler]

I would like to caution that before you extend past the traditional system
(mostly due to Chuquet), you clearly list the name you are using for higher
powers of 1000. Starting from the modern "unvigintillion" (attested from
1853), consensus starts to degenerate. For example, will
you favor "trevigintillion" or "tresvigintillion"? Both versions are "out
there", and both have cogent arguments in their favor. This makes a
difference already at A(19). (I agree with the limit at 10^306 - 1; beyond
that, people just made stuff up. I was one of them.)

On Sun, Apr 23, 2023 at 4:14 PM Neil Sloane <njasloane at gmail.com> wrote:

> Hans,  Thanks for the update on A121064.  If you agree, I think we ought to
> update it to extend the counts out to 10^306 - 1. Could you extend the
> sequence, changing a(13), adding some comments (like those you just posted
> to SeqFan), and maybe also adding links to your "dictionary" pages?
>
> This will remove one ugly thing about the current version, the limit of
> 10^66 .  A limit of 10^306 is still regrettable, but it's a lot better than
> 10^66 !
>
>
> If you can revise A121064, I'll handle the clone I created today (identical
> except at a(4)).  I won't do more than change the terms and refer to your
> version for details.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Sun, Apr 23, 2023 at 3:52 PM Hans Havermann <gladhobo at bell.net> wrote:
>
> > NJAS: "Thanks for mentioning A121064."
> >
> > I finally located my Mathematica notebook on this. I had actually
> > calculated many more terms than the a(0) - a(21) indicated in the
> sequence
> > but my programming is such a mess of increasingly complicated
> done-by-hand
> > logical constructs that I was very fearful of having erred at some point.
> > Here, for the record, are my 2012 calculated a(22) - a(45): 7388, 10176,
> > 14097, 20751, 31104, 46325, 68951, 103898, 161543, 253777, 395341,
> 605405,
> > 910275, 1356377, 2008154, 2949760, 4292046, 6186018, 8888396, 12813090,
> > 18584434, 27119969, 39714742, 58291306. I'm hopeful that some
> enterprising
> > programmer out there can reproduce at least some of these.
> >
> > Being aware that the above are "limited to numbers < 10^66", in 2021 I
> > attempted to recalculate the sequence based on Mathematica's then-new,
> > increased limit of English Integer expressions up to (but not including)
> > 10^306. The new limit means that a(13) is no longer 85, but rather 89,
> > because our larger number range allows for "centillion" (of which there
> are
> > 4) to show. I did not create a replacement for A121064 because I was
> > hopeful Mathematica might incorporate constructs to allow names for
> 10^306
> > and larger. That hasn't happened (yet).
> >
> > But I did create "A dictionary of American English integer names (by
> > letter count)":
> >
> >
> >
> https://gladhoboexpress.blogspot.com/2021/06/a-dictionary-of-american-english.html
> >
> > ... for expressions up to 13 letters and the follow-up "14- to 40-letter
> > integer names":
> >
> >
> >
> http://gladhoboexpress.blogspot.com/2021/06/14-to-40-letter-integer-names.html
> >
> > ... with links to full alphabetically-sorted name lists for 14- to
> > 32-letter names and zip-files for 33- to 40-letter names.
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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