Add Proth number to maths (TheAlgorithms#5246)

* Add Proth number to maths

* Add test for 0 and more informative output

* Fixing test failure issue - unused variable

* Update proth_number.py

Co-authored-by: Christian Clauss <[email protected]>

maths/proth_number.py

@@ -0,0 +1,77 @@
+"""
+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:
+ block_index = number // 3
+ """
+ +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 = math.log(block_index, 2) + 2
+ block_index = int(block_index)
+
+ proth_list = [3, 5]
+ proth_index = 2
+ increment = 3
+ for block in range(1, block_index):
+ for move 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__":
+ 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}")