Project Euler: problem 2

September 16, 2011
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(This article was first published on We think therefore we R, and kindly contributed to R-bloggers)



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.


# Inititae a vector x with two values 1 and 2, the starting points for the Fibonacci series 
x <- c(1,2)
length(x)


# Take an object “i”, with a starting value of 1. 
# This object will be used to as an index for the vector “x”. 
# We continue to add# the (n – 1)th term  and the (n – 2)th term
# to get the nth term. 
# This process continues as long as an element of vector x with 
# index value “i” just crosses the 4,000,000 mark.
i <- 1
while (x[i] < 4000000){i <- i + 1
                        x.index <- length(x)
                        x[x.index + 1] <- x[x.index] + x[x.index – 1]}
x

# Sum the even values of the Fibonacci series thus obtained
sum(x[x %% 2 == 0])


Answer : 4613732

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