sol1.py

"""
Problem 44: https://projecteuler.net/problem=44

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?
"""


defis_pentagonal(n: int) ->bool:
"""
 Returns True if n is pentagonal, False otherwise.
 >>> is_pentagonal(330)
 True
 >>> is_pentagonal(7683)
 False
 >>> is_pentagonal(2380)
 True
 """
root= (1+24*n) **0.5
return ((1+root) /6) %1==0


defsolution(limit: int=5000) ->int:
"""
 Returns the minimum difference of two pentagonal numbers P1 and P2 such that
 P1 + P2 is pentagonal and P2 - P1 is pentagonal.
 >>> solution(5000)
 5482660
 """
pentagonal_nums= [(i* (3*i-1)) //2foriinrange(1, limit)]
fori, pentagonal_iinenumerate(pentagonal_nums):
forjinrange(i, len(pentagonal_nums)):
pentagonal_j=pentagonal_nums[j]
a=pentagonal_i+pentagonal_j
b=pentagonal_j-pentagonal_i
ifis_pentagonal(a) andis_pentagonal(b):
returnb

return-1


if__name__=="__main__":
print(f"{solution() =}")