Problem 68

Erdős Problem #68: declared status 'open'. Formalized: yes. Is$$\sum_{n\geq 2}\frac{1}{n!-1}$$irrational? Current best: Weisenberg has observed that this sum can also be written as$$\sum_{k\geq 1}\sum_{n\geq 2}\frac{1}{(n!)^k}.$$Erd\H{o}s [Er88c] notes that $\sum \frac{1}{n!+t}$ should be transcendental for every integer $t$. Prize: no. OEIS: A331373. Tags: irrationality, number theory.