





import math





def lowerCAmelCase__(__snake_case							)       ->   int:







	'''simple docstring'''







	if not isinstance(__snake_case ,__snake_case							):
		lowerCamelCase__              =	F'Input value of [number={number}] must be an integer'
		raise TypeError(__snake_case							)

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

		lowerCamelCase__              =	[3, 5]
		lowerCamelCase__              =	2
		lowerCamelCase__              =	3
		for block in range(1 ,__snake_case							):
			for _ in range(__snake_case							):
				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):
						_a						=   0
						try:
									_a						=   proth(number)
						except ValueError:
									print(f"""ValueError: there is no {number}th Proth number""")
									continue

						print(f"""The {number}th Proth number: {value}""")










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


_a						=   {
    "configuration_gpt_neo": ["GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP", "GPTNeoConfig", "GPTNeoOnnxConfig"],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_a						=   [
			    "GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST",
			    "GPTNeoForCausalLM",
			    "GPTNeoForQuestionAnswering",
			    "GPTNeoForSequenceClassification",
			    "GPTNeoForTokenClassification",
			    "GPTNeoModel",
			    "GPTNeoPreTrainedModel",
			    "load_tf_weights_in_gpt_neo",
			]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_a						=   [
			    "FlaxGPTNeoForCausalLM",
			    "FlaxGPTNeoModel",
			    "FlaxGPTNeoPreTrainedModel",
			]


if TYPE_CHECKING:
			from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_gpt_neo import (
						    GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
						    GPTNeoForCausalLM,
						    GPTNeoForQuestionAnswering,
						    GPTNeoForSequenceClassification,
						    GPTNeoForTokenClassification,
						    GPTNeoModel,
						    GPTNeoPreTrainedModel,
						    load_tf_weights_in_gpt_neo,
						)

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
			import sys

			_a						=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



