def problem45():
n = 40755
while True:
n = hexagonal(inv_hexagonal(n)+1)
if is_pentagonal(n) and is_trigonal(n):
return n
from math import sqrt
from eulerhelper import hexagonal, inv_hexagonal
from eulerhelper import is_trigonal, is_pentagonal
assert 40755 == hexagonal(inv_hexagonal(40755))
assert is_trigonal(40755) and is_pentagonal(40755)
def problem45():
n = 40755
while True:
n = hexagonal(inv_hexagonal(n)+1)
if is_pentagonal(n) and is_trigonal(n):
return n
print problem45()
