题目171：寻找各个数位的平方之和也是个平方数的数字
Finding numbers for which the sum of the squares of the digits is a squareFor a positive integer n, let f(n) be the sum of the squares of the digits (in base 10) of n, e.g.
f(3) = 32 = 9,
f(25) = 22 + 52 = 4 + 25 = 29,
f(442) = 42 + 42 + 22 = 16 + 16 + 4 = 36
Find the last nine digits of the sum of all n, 0 < n < 1020, such that f(n) is a perfect square.
题目：
对正整数 n，定义 f(n) 为它的各个数位的平方之和，例如：
f(3) = 32 = 9,
f(25) = 22 + 52 = 4 + 25 = 29,
f(442) = 42 + 42 + 22 = 16 + 16 + 4 = 36
对于 0 < n < 1020， 中所有满足 f(n) 是完全平方数的 n，求这些 n 之和的最后 9 位数字。
动态规划题目
from itertools import zip_longest as zip_l, chain, repeat
def do_fast(size = 20, m = 10**9, b = 10):
S = * (1 + (b-1)**2)
for d in range(b): S = d
for k in range(1, size):
loop =
S =
s = sum( for j in range(int((len(S) - 1)**0.5) + 1)]) % m
all_ones = 10**size // 9 % m
return all_ones * s % m
print(do_fast())
142989277
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