'''
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle	 	Tn=n(n+1)/2	 	1, 3, 6, 10, 15, ...
Pentagonal	 	Pn=n(3n−1)/2	1, 5, 12, 22, 35, ...
Hexagonal	 	Hn=n(2n−1)	 	1, 6, 15, 28, 45, ...
It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.
'''

# Observe that every other triangle number is also a hexagonal number, so the 1st, the 3rd, 5th, etc.
# So we only need to check all the uneven n triangle numbers to be pentagonal

# In addition, we can check if a number is pentagonal by checking if sqrt(1 + 24 n) % 6 == 5

import math

def t(n):
    return n * (n+1) / 2

def isPentagonal(x):
    return math.sqrt(1 + 24 * x) % 6 == 5

def main():
    print("Hello this is Patrick")

    n = 287
    while not isPentagonal(t(n)):
        n += 2
    
    print(t(n))

if __name__ == "__main__":
    main()