def compute():
i = 2
while True:
i += 1
m = i * (3 * i - 1) // 2
for j in range(2, i):
n = j * (3 * j - 1) // 2
if is_pentagonal(m+n) and is_pentagonal(m-n):
return m - n
# 1533776805
import euler
n = 144
while True:
h = n * (2 * n - 1)
if euler.is_pentagonal(h) and euler.is_triangular(h):
print h
break
n += 1
def compute():
n = 144
while not (is_triangular(n * (2 * n - 1)) and is_pentagonal(n * (2 * n - 1))):
n += 1
return n * (2 * n - 1)
# 5482660
import euler
i = 1
p = [0]
m = None
while m is None:
p.append(i * (3 * i - 1) / 2)
if p[i] % 2 == 0:
j = 1
while i > j:
if p[j] % 2 == 0 and euler.is_pentagonal(p[i] - p[j]) and \
euler.is_pentagonal(p[i] + p[j]):
m = p[i] - p[j]
break
j += 1
i += 1
print m
from itertools import count, takewhile from euler import pentagonal, is_pentagonal result = () pentagonals_generated = set() for n in count(1): pentagon_n = pentagonal(n) pentagonals_generated.add(pentagon_n) for pentagon_sub_n in takewhile(lambda p_sub_n: p_sub_n < pentagon_n, pentagonals_generated): pentagon_diff = pentagon_n - pentagon_sub_n if pentagon_diff in pentagonals_generated: pentagon_sum = pentagon_n + pentagon_sub_n if is_pentagonal(pentagon_sum): result = (pentagon_diff, n, pentagon_n, pentagon_sub_n, pentagon_sum) break else: continue break print "D: %d, n: %d, pentagon_n: %d, pentagon_sub_n: %d, pentagon_sumb: %d" % result
from itertools import count from euler import pentagonal, is_pentagonal result = () for n in count(1): pentagon_n = pentagonal(n) for sub_n in xrange(1, n): pentagon_sub_n = pentagonal(sub_n) pentagon_diff = pentagon_n - pentagon_sub_n if is_pentagonal(pentagon_diff): pentagon_sum = pentagon_n + pentagon_sub_n if is_pentagonal(pentagon_sum): result = (pentagon_diff, n, sub_n, pentagon_n, pentagon_sub_n, pentagon_sum) break else: continue break print "D: %d, n: %d, sub_n: %d, pentagon_n: %d, pentagon_sub_n: %d, pentagon_sumb: %d" % result