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Problem45.py
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Problem45.py
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'''
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.
'''
from __future__ import division
from math import sqrt
def genTriangular():
'''Generate an infinite list of triangular numbers'''
triangleSum = 1
counter = 1
while True:
yield triangleSum
counter += 1
triangleSum += counter
def isPentagonal(P):
checkNum = (1 + sqrt(1 + 24*P))/6
return int(checkNum) == checkNum
def isHexagonal(H):
checkNum = (1 + sqrt(1+8*H))/4
return int(checkNum) == checkNum
for triNum in genTriangular():
if isPentagonal(triNum) and isHexagonal(triNum):
print triNum