project euler – problem 49
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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another. There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence. What 12-digit number do you form by concatenating the three terms in this sequence?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | n <- 10^4:10^3
prime <- n[gmp::isprime(n) != 0]
pl <- lapply(prime,function(i) unlist(strsplit(as.character(i), split="")))
flag <- 0
for (i in seq_along(pl)) {
x <- pl[[i]]
maxP <- prime[i]
pl <- pl[-i]
prime <- prime[-i]
idx <- unlist(lapply(pl, function(i) all(x %in% i) & all(i %in% x)))
idx <- which(idx)
if (length(idx) >= 2) {
sel <- prime[idx]
diff <- maxP-sel
for (j in 1:length(diff)) {
m <- which(diff == 2* diff[j])
if (length(m) >= 1) {
minP <- sel[m[length(m)]]
midP <- sel[j]
flag <- 1
break
}
}
}
if(flag) {
break
}
}
ans <- paste(c(minP, midP, maxP), collapse="")
print(ans) |
> system.time(source("problem49.R")) system.time(source("problem49.R"))
[1] "296962999629"
user system elapsed
0.25 0.00 0.25
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