euler.R

# Problem #1
# Answer: 233168
#
# If we list all the natural numbers below 10 that are multiples of 3
# or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
#
# Find the sum of all the multiples of 3 or 5 below 1000.

xs <- 1:999
euler1 <- sum(xs[xs %% 3 == 0 | xs %% 5 == 0])


# Problem #2
# Answer:
#
# Each new term in the Fibonacci sequence is generated by adding the
# previous two terms. By starting with 1 and 2, the first 10 terms
# will be:
#
#     1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
#
# Find the sum of all the even-valued terms in the sequence which do
# not exceed four million.

e2fib <- function(n) {
    fibs <- c(length=n)
    fibs[1] <- 1
    fibs[2] <- 2
    for (i in 3:n) {
        fibs[i] <- fibs[i - 1] + fibs[i - 2]
        if (fibs[i] > n) {
            break
        }
    }
    fibs
}
xs <- e2fib(4E6)
euler2 <- sum(xs[xs %% 2 == 0])