Project Euler 49

problem

Arithmetic progressions 1487, 4817, 8147 with a term difference of 3330 have two unusual properties:

(i) Each of the three terms is a prime number. (ii) Each term is represented by a permutation of another term. There is no sequence with this property for 1, 2 and 3 digit prime numbers, but there is another for the 4 digit increment sequence.

Now, find the 12-digit number that concatenates the three terms of this sequence. http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2049

Answer

  1. Create a dictionary that represents the number of each digit with count_numbers.
  2. For all arithmetic progressions of prime numbers, check if the dictionaries by count_numbers of the numbers contained in the sequence are equal.

Click here for mymath https://github.com/cof01/ProjectEuler/blob/master/mymath.py

# coding: utf-8
import math
from mymath import get_primes,is_prime

def count_numbers(n):
    ret = {i:0 for i in range(10)}
    for s in str(n):
        ret[int(s)] += 1
    return ret

def check(p,diff,pri):
    p1, p2, p3 = p, p+diff, p+diff*2
    if not is_prime(p2, pri):
        return False
    if not is_prime(p3, pri):
        return False
    if count_numbers(p1) == count_numbers(p2) == count_numbers(p3):
        return True
    else:
        return False

def main():
    MIN, MAX = 10**3, 10**4
    pri = get_primes(MAX)
    ans = []
    for p in pri['list']:
        if p <= MIN:
            continue
            
        for diff in range(2, (MAX-p)//2, 2):
            if check(p,diff,pri):
                ans.append([p, p+diff, p+diff*2])
                break
    print ans
main()

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