[seqfan] Re: Mathematica code in A080777

[M. F. Hasler]

On Sun, Jun 13, 2021, 13:14 Hans Havermann <gladhobo at bell.net> wrote:

> https://oeis.org/A080777


Kudos for putting a clickable link that saves painful copy paste, app
switching, Google search and other frustration, esp. for people trying to
follow with smartphones.

correction of IntegerName[n,"Words"] which previously had provided
> incorrect power names for numbers >= 10^102 (adding a spurious "s"
> pluralization). While not at play in A080777, ...
>

These sequences are some (RECORD-like, maybe "ORDINAL"?) transform of the
underlying sequence
"a(n) = number of letters in the English name for n"
which is not cited /referenced in *any* of this family of inter-linked
sequences which only xref to each other among themselves.
All the problems you discuss here belong to that sequence (I think it's
oeis.org/A005589 <http://oeis.org/>) and not to its various derivatives.
These derivatives should not redo the same job using elementary mathematica
functions to convert numbers to English and then count letters, but rely on
that oeis function which should provide an  efficient  implementation where it
belongs.
It should use A005589 <http://oeis.org/> even if one has a more
intelligent, non-brute force approach, which seems to be the case here,
looking at the second half of your "illustration of growth" a-file.

-Maximilian