mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
74 lines
1.9 KiB
Python
74 lines
1.9 KiB
Python
"""
|
|
Calculate the nth Proth number
|
|
Source:
|
|
https://handwiki.org/wiki/Proth_number
|
|
"""
|
|
|
|
import math
|
|
|
|
|
|
def proth(number: int) -> int:
|
|
"""
|
|
:param number: nth number to calculate in the sequence
|
|
:return: the nth number in Proth number
|
|
Note: indexing starts at 1 i.e. proth(1) gives the first Proth number of 3
|
|
>>> proth(6)
|
|
25
|
|
>>> proth(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Input value of [number=0] must be > 0
|
|
>>> proth(-1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Input value of [number=-1] must be > 0
|
|
>>> proth(6.0)
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: Input value of [number=6.0] must be an integer
|
|
"""
|
|
|
|
if not isinstance(number, int):
|
|
raise TypeError(f"Input value of [number={number}] must be an integer")
|
|
|
|
if number < 1:
|
|
raise ValueError(f"Input value of [number={number}] must be > 0")
|
|
elif number == 1:
|
|
return 3
|
|
elif number == 2:
|
|
return 5
|
|
else:
|
|
"""
|
|
+1 for binary starting at 0 i.e. 2^0, 2^1, etc.
|
|
+1 to start the sequence at the 3rd Proth number
|
|
Hence, we have a +2 in the below statement
|
|
"""
|
|
block_index = int(math.log(number // 3, 2)) + 2
|
|
|
|
proth_list = [3, 5]
|
|
proth_index = 2
|
|
increment = 3
|
|
for block in range(1, block_index):
|
|
for _ in range(increment):
|
|
proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1])
|
|
proth_index += 1
|
|
increment *= 2
|
|
|
|
return proth_list[number - 1]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
for number in range(11):
|
|
value = 0
|
|
try:
|
|
value = proth(number)
|
|
except ValueError:
|
|
print(f"ValueError: there is no {number}th Proth number")
|
|
continue
|
|
|
|
print(f"The {number}th Proth number: {value}")
|