#' Fly Straight
#'
#' TODO: write a nice description
#'
#' @param n The number of terms of the sequence to generate.
#'
#' @examples
#' fs <- fly_straight(1000)
#' plot(fs)
#'
#' @references This sequence in the On-Line Encyclopedia of Integer Sequences:
#' \href{https://oeis.org/A133058}{A133058}.
#'
#' The Numberphile video featuring Neil Sloane and Brady Haran:
#' \href{https://youtu.be/pAMgUB51XZA}{Amazing Graphs}.
#'
#' @export
fly_straight <- function(n) {
stopifnot(n > 1)
a <- c(1, 1, rep(NA, n - 2))
for (i in 2:n) {
gcd_ <- gcd(i, a[i - 1])
if (gcd_ == 1) {
a[i] <- a[i - 1] + i + 1
} else {
a[i] <- a[i - 1] / gcd_
}
}
data.frame(x = 0:n, y = c(1, a))
}
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