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#!/usr/bin/env python
# -*- coding: utf-8 -*-
import math
def is_pentagonal(num):
return (math.sqrt(24 * num + 1) + 1) % 6 == 0
def pentagonal_numbers():
index = 1
pentagonal_nums = []
while True:
pentagonal_num = index * (3 * index - 1) // 2
pentagonal_nums.append(pentagonal_num)
for j in range(index - 1, 0, -1):
if is_pentagonal(pentagonal_num - pentagonal_nums[j - 1]) and is_pentagonal(
pentagonal_num + pentagonal_nums[j - 1]
):
return pentagonal_nums[j - 1], pentagonal_num
index += 1
pair = pentagonal_numbers()
print(f"Pair of Pentagon Numbers: {pair[0]}, {pair[1]}")
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