R: Project Euler 50-59

problem50.R

library(pracma)
library(gmp)

p <- primes(1e6%/%21)

answer <- 0
maxLength <- 0
while (length(p) > 0) {
	x <- rev((x <- cumsum(p))[x < 1e6])
	while (length(x) > 0) {
		if (length(x) <= maxLength) break
		if (isprime(x[1]) > 0) {
			if (length(x) > maxLength) {
				answer <- x[1]
				maxLength <- length(x)
			}
			break
		}
		x <- x[-1]
	}
	p <- p[-1]
}
answer

problem52.R

nextNum <- function(n) {
	x <- 6*(n+3); y <- floor(log10(x))
	if (y == floor(log10(n))) return(n+3) else 10^y+2
}

digits <- function(n) n %/% 10^(floor(log10(n)):0) %% 10

answer <- function(n) {
	d <- digits(n)
	setequal(d, digits(2*n)) &&
	setequal(d, digits(3*n)) &&
	setequal(d, digits(4*n)) &&
	setequal(d, digits(5*n)) &&
	setequal(d, digits(6*n))
}

n <- 1e5+2
repeat {if (answer(n)) break; n <- nextNum(n)}
n

problem53.R

answer <- 0
for (n in 1:100) {
	x <- choose(n, 1:n)
	answer <- answer + length(x[x > 1e6])
}
answer

problem55.R

library(gmp)

digits <- function(n) strsplit(as.character(n), "")[[1]]

addrev <- function(n) {
	m <- rev(digits(n))
	while (m[1] == "0") m <- m[-1]
	n + as.bigz(paste(m, collapse=""))
}

palindrome <- function(n) {d <- digits(n); all(d == rev(d))}

Lychrel <- function(n) {
	iterations <- 0
	repeat {
		if (iterations >= 50) return(TRUE)
		iterations <- iterations + 1
		n <- addrev(n)
		if (palindrome(n)) return(FALSE)
	}
}

length(Filter(Lychrel, 1:10000))

problem56.R

library(gmp)

f <- function (x, y) {
	n <- pow.bigz(x, y)
	sum(as.numeric(strsplit(as.character(n), "")[[1]]))
}

answer <- 0
for (x in 2:99) for (y in 2:99) {
	n <- f(x, y)
	if (n > answer) answer <- n
}
answer

problem58.R

library(gmp)

side <- 7
primes <- 8
total <- 13

repeat {
	if (primes/total < 0.1) break
	side <- side + 2
	a <- side^2 - side + 1
	b <- a - side + 1
	c <- b - side + 1
	primes <- primes + length((p <- sapply(c(a,b,c), isprime))[p > 0])
	total <- total + 4
}
side