Letters of Names of Numbers in Alphabetical Order/French
Theorem
When written in French, the only integers the letters of whose name appear in alphabetical order are:
\(\displaystyle 2:\) | \(\) | \(\displaystyle \) | deux | ||||||||||
\(\displaystyle 5:\) | \(\) | \(\displaystyle \) | cinq | ||||||||||
\(\displaystyle 10:\) | \(\) | \(\displaystyle \) | dix | ||||||||||
\(\displaystyle 100:\) | \(\) | \(\displaystyle \) | cent |
This sequence is A277438 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Historical Note
The integers the letters of whose names appear in alphabetical order when written in French were noticed in $1998$ by Matt Westwood on reading in Curious and Interesting Numbers, 2nd ed. by David Wells ($1997$) that $40$ was the only such number in English.
It is more than probable that others had noticed it before this, but no evidence of this has yet been unearthed.
It crops up online on occasion, for example https://www.mathsisfun.com/puzzles/alphabetical-order-solution.html
The result even appears in contemporary literature: The Curse of the Ice Serpent by Jon Mayhew (2015) features a puzzle whose solution depends on it.