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

[Neil Sloane]

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.
>
> --
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>