#!/usr/bin/python
# coding: UTF-8
"""
@author: CaiKnife
Triangular, pentagonal, and hexagonal
Problem 45
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(3n1)/2 1, 5, 12, 22, 35, ...
Hexagonal Hn=n(2n1) 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 euler import triangle_number, pentagon_number, hexagon_number
p = set(pentagon_number(i) for i in range(1, 100000))
h = set(hexagon_number(i) for i in range(1, 100000))
for i in range(286, 100000):
t = triangle_number(i)
if t in p and t in h:
print t
break
#!/usr/bin/python
# coding: UTF-8
"""
@author: CaiKnife
Pentagon numbers
Problem 44
Pentagonal numbers are generated by the formula, Pn=n(3n1)/2. The first ten pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 22 = 48, is not pentagonal.
Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference is pentagonal and D = |Pk Pj| is minimised; what is the value of D?
"""
from itertools import combinations
from operator import itemgetter, add, sub
from euler import pentagon_number
pentagons = set(pentagon_number(n) for n in range(1, 3000))
c = combinations(pentagons, 2)
for p in c:
if add(*p) in pentagons and abs(sub(*p)) in pentagons:
print abs(sub(*p))