The 100 Doors Puzzle in R at Rosetta Code

From time to time I see a puzzle at Rosetta Code that interests me, and I post an R solution for it.  This time it was the 100 doors puzzle.

Problem: You have 100 doors in a row that are all initially closed. You make 100 passes by the doors. The first time through, you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, …). The third time, every 3rd door (door #3, #6, #9, …), etc, until you only visit the 100th door.

Question: What state are the doors in after the last pass? Which are open, which are closed?

The code for this in R is pretty simple:

# UNOPTIMIZED
doors_puzzle <- function(ndoors=100,passes=100) {
    doors <- rep(FALSE,ndoors)
    for (ii in seq(1,passes)) {
        mask <- seq(0,ndoors,ii)
        doors[mask] <- !doors[mask]   
    }
    return (which(doors == TRUE))
}

doors_puzzle()

## optimized version... we only have to to up to the square root of 100
seq(1,sqrt(100))**2