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54 lines
1.4 KiB
Python
54 lines
1.4 KiB
Python
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"""After 40755, what is the next triangle number that is also pentagonal and hexagonal?
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Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
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Triangle Tn=n(n+1)/2 1, 3, 6, 10, 15, ...
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Pentagonal Pn=n(3n-1)/2 1, 5, 12, 22, 35, ...
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Hexagonal Hn=n(2n-1) 1, 6, 15, 28, 45, ...
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It can be verified that T285 = P165 = H143 = 40755.
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Find the next triangle number that is also pentagonal and hexagonal.
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"""
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def triangle_generator(start = 0):
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n = start
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while True:
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n = n + 1
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yield n * (n + 1) / 2
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def pentagonal_generator(start = 0):
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n = start
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while True:
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n = n + 1
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yield n * (3 * n - 1) / 2
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def hexagonal_generator(start = 0):
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n = start
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while True:
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n = n + 1
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yield n * (2 * n - 1)
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MIN = 40755
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def main():
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pent_count = 0
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tri_count = 0
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for hex in hexagonal_generator():
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if hex <= MIN:
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continue
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# Catch up the other generators
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for pent in pentagonal_generator(pent_count):
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pent_count = pent_count + 1
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if pent >= hex:
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break
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if pent > hex:
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continue
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for tri in triangle_generator(tri_count):
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tri_count = tri_count + 1
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if tri >= hex:
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break
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if tri > hex:
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continue
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print 'Next number is:', hex
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break
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if __name__ == '__main__':
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main()
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