'''
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http://projecteuler.net/problem=136
The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2 y2 z2 = n, has exactly one solution when n = 20:
132 102 72 = 20
In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.
How many values of n less than fifty million have exactly one solution?
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'''
import numpy as np
from euler.problem135 import num_solutions
from euler.problem146 import isp
if __name__ == "__main__":
# Testing, problem 136
a = np.where(num_solutions(300) == 1)[0]
print a
m = map(lambda x: x / 4, filter(lambda x: not isp(x), a))
print m
print filter(lambda x: x >= 3 and not isp(x), m)
print len(np.where(num_solutions(5 * 10 ** 7) == 1)[0])
def is_prime_proof_and_contains_target(x):
s = str(x)
return TARGET in s and \
not any(isp(int(s[:i] + d + s[i + 1:]))
for i in xrange(len(s))
for d in (NON_ZERO_DIGITS if i == 0 else DIGITS) if d != s[i])