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

[Hans Havermann]

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.