def problem_44():
# upper limit determined experimentally. Haven't found an analytical way to determine it
pentagonals = list(pentagonal_numbers(count=3000))
candidates = list()
for a in pentagonals:
for b in pentagonals:
if a == b:
continue
if is_pentagonal(abs(a - b)) and is_pentagonal(a + b):
# the first such pair we find should be smallest difference, so we can finish
print(abs(a - b))
return
def problem_45():
# We can ignore the triangle number aspect of the problem altogether, since all hexagonal
# numbers are also triangular numbers
# get an iterator for hexagonal numbers, and skip them up to 40755, since we want to identify
# a number after that point
hexagonals = hexagonal_numbers()
while next(hexagonals) < 40755:
pass
for n in hexagonals:
if is_pentagonal(n):
print(n)
break
