37 lines
909 B
Python
37 lines
909 B
Python
#!/usr/bin/env python3
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# Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
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#
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# Triangle T_n=n(n+1)/2 1, 3, 6, 10, 15, ...
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# Pentagonal P_n=n(3n−1)/2 1, 5, 12, 22, 35, ...
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# Hexagonal H_n=n(2n−1) 1, 6, 15, 28, 45, ...
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#
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# It can be verified that T_285 = P_165 = H_143 = 40755.
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#
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# Find the next triangle number that is also pentagonal and hexagonal.
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from projecteuler import is_pentagonal, timing
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@timing
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def p045() -> None:
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found = 0
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i = 143
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while not found:
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i = i + 1
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# Hexagonal numbers are also triangle numbers, so it's sufficient
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# to generate hexagonal numbers (starting from H_144) and check if
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# they're also pentagonal.
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n = i * (2 * i - 1)
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if is_pentagonal(n):
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found = 1
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print('Project Euler, Problem 45')
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print(f'Answer: {n}')
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if __name__ == '__main__':
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p045()
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