#!/usr/bin/env python3
"""
Created on 18 Sep 2021

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for problem 49 of Project Euler
https://projecteuler.net/problem=49
"""

from utils import timeit, list_primes


@timeit("Problem 49")
def compute():
    """
    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?
    """
    ans = []
    primes_list = sorted(set(list_primes(10_000)) - set(list_primes(1_000)))

    for number in primes_list:
        if set(list(str(number))) == set(list(str(number+3330))) == set(list(str(number+6660))):
            if number+3330 in primes_list and number+6660 in primes_list:
                ans.append(str(number)+str(number+3300)+str(number+6660))
    # return the second one
    return ans[1]


if __name__ == "__main__":

    print(f"Result for Problem 49: {compute()}")