Python Implementation of Problem 44
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Includes
math.is_pentagonal()math.pentagonal()
Problem Solution
Project Euler Problem 44
Problem:
Pentagonal numbers are generated by the formula, Pn=n(3n−1)/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 are pentagonal and D = |Pk − Pj|
is minimised; what is the value of D?
1"""
2Project Euler Problem 44
3
4Problem:
5
6Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:
7
81, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
9
10It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.
11
12Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = ``|Pk − Pj|``
13is minimised; what is the value of D?
14"""
15from itertools import islice
16
17from .lib.math import is_pentagonal, pentagonal
18
19
20def main() -> int:
21 D = 1_000_000_000_000
22 pentagonals = [pentagonal(x) for x in range(1, 2_500)]
23 for idx, k in enumerate(pentagonals):
24 for j in islice(pentagonals, idx):
25 if is_pentagonal(j + k) and is_pentagonal(k - j):
26 D = min((D, abs(k - j)))
27 return D