R: Project Euler 20-29

problem20.R

library(gmp)

n <- factorialZ(100)
sum(n %/% pow.bigz(10, (floor(log10(n)):0)) %% 10)

problem21.R

max <- 10000

x <- rep(1, max)
for (i in 2:(max/2)) {
	j <- 2:(max/i) * i
	x[j] <- x[j] + i
}

y <- (1:max)[x[x] == 1:max]
y <- y[y != x[y]]
sum(y[!is.na(y)])

problem22.R

name <- sort(scan("names.txt", what="character", sep=",", na.strings = ""))
name <- strsplit(name, "")
f <- function(x, y) x + which(LETTERS %in% y)
value <- Vectorize(function(s) Reduce(f, s, 0))
sum(value(name) * 1:length(name))

problem23.R

max <- 28123
 
sumDivisors <- rep(1, max)
for (i in 2:(max/2)) {
	j <- 2:(max/i) * i
	sumDivisors[j] <- sumDivisors[j] + i
}
 
nums <- 1:max

abundants <- nums[sumDivisors > nums]
for (n in abundants) {
	nums[abundants[abundants <= max-n] + n] <- 0
}

sum(nums)

problem24.R

n <- 1e6; d <- 0:9; answer <- 0
for (f in factorial(9:0)) {
	x <- (n-1)%/%f
	n <- n - x*f
	answer <- 10*answer + d[x+1]
	d <- d[-(x+1)]
}
answer

problem25.R

library(gmp)

n <- 1; limit <- pow.bigz(10,999)
while (fibnum(n) < limit) n <- n+1
n

problem26.R

f <- function(n) {
	x <- 10^(floor(log10(n))+1)
	v <- numeric(0)
	repeat {
		y <- x %% n
		if (y == 0) return(0)
		if (y %in% v) return(length(v))
		v <- c(v, y)
		x <- 10*y
	}
}

which.max(sapply(1:999, f))

problem27.R

library(gmp)
 
a <- seq(-999, 1000, by=2)
b <- primes(1000)
f <- Vectorize(function(a, b) {
	if (a+b < 1) return(0)
	n <- 0
	while (isprime(n^2+n*a+b)) n <- n+1
	n
})
x <- outer(a, b, f)
ind <- which(x == max(x), arr.ind=TRUE)
a[ind[1]] * b[ind[2]]

problem28.R

n <- seq(3, 1001, by=2)
sum(4*(n^2-n+1)) + 1

problem29.R

library(gmp)
length(unique(as.character(as.vector(outer(2:100, 2:100, pow.bigz)))))