Project Euler — problem 2

Almost my time for bed. Just write a quick solution on the second problem of Project Euler. Here it is.

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, … By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. 

The solution is straightforward: firstly generate the Fibonacci sequence, then calculate the sum of even numbers.

1
2
3
4
5
6
7
8
9
10
11
12
13
14

fibonacci <- numeric()
fibonacci[1] <- 1
fibonacci[2] <- 2
i <- 3
repeat {
  fibonacci[i] <- fibonacci[i-1] + fibonacci[i-2]
  if (fibonacci[i] > 4e6) break
  i <- i + 1
}
# calculate the sum
fibonacci <- fibonacci[-length(fibonacci)]   # remove the last term
flag <- fibonacci %% 2 == 0  # find the indexes of even numbers
result <- sum(fibonacci[flag])
cat("The result is:", result, "\n")

I miscalculated twice on this problem. The first was a misunderstanding to calculate the sum the even-indexed terms; the second was just a bug. I guess I was sleepy. I believe there must be some brilliant mathematical ways to solve it. I’ll read the forum later.
Functions used: repeat, break (two flow control commands) and length(), sum().