Project Euler Problem 49

最新推荐文章于 2020-12-08 19:51:26 发布

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最新推荐文章于 2020-12-08 19:51:26 发布

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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?

公差为3330的三项等差序列1487、4817、8147在两个方面非常特别：其一，每一项都是素数；其二，两两都是重新排列的关系。

一位素数、两位素数和三位素数都无法构成满足这些性质的数列，但存在另一个由四位素数构成的递增序列也满足这些性质。

将这个数列的三项连接起来得到的12位数是多少？

def isprime(x):
    if x <= 1:
        return False
    for i in range(2,int(x**0.5+1)):
        if x % i == 0:
            return False
    return True

lst = []
for i in range(1000,10000):
    if isprime(i):
        lst.append(i)
lst2 = []
for x in lst:
    for y in lst[lst.index(x)+1:]:
        if 2*y-x in lst:
            lst2.append([x,y,2*y-x])
for j in lst2:
    if set(str(j[0]))==set(str(j[1]))==set(str(j[2])):
        print(j)