Repunit is a number consisting only of $1$s (here in base $10$).
Examples - $1$, $11$, $11111$.
Goal
Create 10 first repunits $n$-digits long from least possible number instances of numbers $n$.
For example (these are not minimal),
$11 = 2\times2\times2\times2-2-2-2/2$
$111 = 3\times(3\times3\times3 + 3 + 3 + 3) + 3$.
Allowed operators
- Arithmetic $+$, $-$, $\times$, $/$
- Exponentiation of positive rational numbers
- Square root, $n$-th roots of positive rational numbers
- Factorial, Gamma function, subfactorial of integers
Number concatenation is not allowed!
Note: actually, you need only 9 repunits (first ($1$) is trivial, so no need to write it down) - starting with 11 and ending with 1111111111.