YGC

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
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25
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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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