"""Prime permutations

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Problem 49

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?"""

from math import sqrt

from itertools import permutations

from typing import List

from utils import isPrime, nextprime

def permutationsofanumber(number: int) -> List[int]:

return listnums

def arithmetic_sequences(listofnumbers):

return prime_permutations

print("The permuation of the digits of 123 is: ", permutationsofanumber(123))

listofperms2 = sorted(permutationsofanumber(1487))

print("Permutations of 1487", listofperms2)

print("The arithmetric sequences including 1487 that are prime:")

print(arithmetic_sequences(listofperms2))

primes = nextprime()

iprime = next(primes)

pm = set()

while iprime <= 10000:

iprime = next(primes)

pm = pm.union(arithmetic_sequences(permutationsofanumber(iprime)))

print("The 4-digit arithmetric sequences that are all prime are:")

print(pm)