Forum Favourites Tags
More
FAQ Prizes Problem Lists Definitions Links
Forum
Favourites Tags FAQ Prizes Problem Lists Definitions Links
Dual View Random Solved Random Open
OPEN This is open, and cannot be resolved with a finite computation.
Is\[\sum_{n\geq 2}\frac{1}{n!-1}\]irrational?
Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.
The decimal expansion is A331373 in the OEIS. Weisenberg has observed that this sum can also be written as\[\sum_{k\geq 1}\sum_{n\geq 2}\frac{1}{(n!)^k}.\]Erdős [Er88c] notes that $\sum \frac{1}{n!+t}$ should be transcendental for every integer $t$.

View the LaTeX source

This page was last edited 28 September 2025.

External data from the database - you can help update this
Formalised statement? Yes
Related OEIS sequences: A331373

Additional thanks to: Desmond Weisenberg

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #68, https://www.erdosproblems.com/68, accessed 2025-11-16
0 comments on this problem
Order by oldest first or newest first.

All comments are the responsibility of the user. Comments appearing on this page are not verified for correctness. Please keep posts mathematical and on topic.

Log in to add a comment.

Back to the forum