






from __future__ import annotations

from math import pi, sqrt

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float )      ->					tuple:

    if inductance <= 0:
        raise ValueError('''Inductance cannot be 0 or negative''' )

    elif capacitance <= 0:
        raise ValueError('''Capacitance cannot be 0 or negative''' )

    else:
        return (
            "Resonant frequency",
            float(1 / (2 * pi * (sqrt(inductance * capacitance ))) ),
        )


if __name__ == "__main__":
  import doctest

  doctest.testmod()












import math

def      _lowerCamelCase	(						__A    :							int )      ->					int:

    if not isinstance(__A		,		__A ):
        _UpperCAmelCase				:      List[Any]			  =				f'''Input value of [number={number}] must be an integer'''
        raise TypeError(__A )

    if number < 1:
        _UpperCAmelCase				:      Optional[Any]			  =				f'''Input value of [number={number}] must be > 0'''
        raise ValueError(__A )
    elif number == 1:
        return 3
    elif number == 2:
        return 5
    else:
        _UpperCAmelCase				:      Any			  =				int(math.log(number // 3		,		2 ) ) + 2

        _UpperCAmelCase				:      Dict			  =				[3, 5]
        _UpperCAmelCase				:      Tuple			  =				2
        _UpperCAmelCase				:      Dict			  =				3
        for block in range(1		,		__A ):
            for _ in range(__A ):
                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):
    SCREAMING_SNAKE_CASE 							=						0
    try:
      SCREAMING_SNAKE_CASE 							=						proth(number)
    except ValueError:
      print(F'ValueError: there is no {number}th Proth number')
      continue

    print(F'The {number}th Proth number: {value}')




