The Wikipedia page for [unusual number](https://en.wikipedia.org/wiki/Unusual_number) states that the density of that set is $\ln 2$, and that this was proven by Schroeppel in 1972. The only source that I found for that is the [HAKMEM document](https://en.wikipedia.org/wiki/HAKMEM), and there is no proof given there, just the statement. Does anyone know a reference for a proof? Thanks.



How does one prove that the density of unusual numbers is $\ln 2$?
A reference is Greene and Knuth, Mathematics for the Analysis of Algorithms, 3rd ed., pages 95-98. The section of the book containing those pages may be found at <https://link.springer.com/content/pdf/bbm%3A978-0-8176-4729-2%2F1.pdf>


