diff --git a/49/main.py b/49/main.py new file mode 100644 index 0000000..172647a --- /dev/null +++ b/49/main.py @@ -0,0 +1,54 @@ +''' +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? +''' + +import math +import numpy as np +from itertools import permutations + +def sieve(n): + assert n > 1 + + ns = [True] * n + + for i in range(2, math.ceil(np.sqrt(n))): + if ns[i]: + j = pow(i, 2) + + while j < n: + ns[j] = False + j = j + i + + return [i for i,val in enumerate(ns) if val][2:] + +def digitToList(n): + return [int(c) for c in str(n)] + +def listToDigit(l): + res = 0 + for i in l: + res = 10 * res + i + return res + +def main(): + print("Hello this is Patrick") + + primeSet = set(sieve(10000)) - set(sieve(1000)) + primeList = list(primeSet) + + for p in primeList: + perms = list(set(map(listToDigit, list(permutations(digitToList(p)))))) + + for perm in perms: + if p != perm and perm in primeSet: + if max(p, perm) + abs(p - perm) in primeSet and max(p, perm) + abs(p - perm) in perms: + print(min(p, perm), max(p, perm), max(p, perm) + abs(p - perm)) + + + +if __name__ == "__main__": + main() \ No newline at end of file