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infinite_sequences.py
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import powers
import loop_formula
import sequence_inverter
import trailing_bit_generator
import p_adics
NORMAL_SEQUENCE: list[int] = []
for i in range(4096):
for bit in format(i, "b"):
NORMAL_SEQUENCE.extend([2] if bit == "0" else [4])
def large_division(ratio: tuple[int, int], digits: int) -> str:
quotient = str(ratio[0]*powers.POWERS_OF_10[digits] // ratio[1])
quotient = "0"*(digits - len(quotient)) + quotient
quotient = quotient[:-digits] + "." + quotient[-digits:]
for i in range(len(quotient)):
if quotient.endswith("0"):
quotient = quotient[:-1]
else:
break
return quotient
def expanding_powers():
for i in range(100):
result = loop_formula.get_loop(powers.POWERS_OF_2[1:i+2])
# print(f"[2 ... {powers.POWERS_OF_2[i+1]}]: {large_division(result, 100)}, {result[0]}/{result[1]}")
print(f"[2 ... {powers.POWERS_OF_2[i+1]}]: {large_division(result, 100)}")
def normal_of_2_and_4_trailing_bits():
sequence = NORMAL_SEQUENCE[:32]
values: list[tuple[int, int]] = []
binary_strings: list[str] = []
max_string_length = 0
for i in range(len(sequence)):
value = trailing_bit_generator.generate_trailing_bits(sequence[:i+1], 1)
values.append(value)
binary_string = trailing_bit_generator.format_to_binary(value)
binary_strings.append(binary_string)
max_string_length = max(max_string_length, len(binary_string))
for i in range(len(sequence)):
binary_string = binary_strings[i]
print(f"{" "*(max_string_length - len(binary_string))}{binary_string}")
def normal_of_2_and_4_loop():
for i in range(0, len(NORMAL_SEQUENCE), 250):
sequence = NORMAL_SEQUENCE[:i+1]
result = loop_formula.get_loop(sequence)
print(f"{len(sequence)}: {large_division(result, 100)}")
def sequence_7_loop():
sequence = [2,2,4,8,16]
while True:
sequence.append(4)
result = loop_formula.get_loop(sequence)
print(f"{len(sequence)}: {large_division(result, 100)}")
def test_sequence_inverter_on_loop():
# sequence: list[int] = [2,2,8,4]
sequence: list[int] = [2,2,4,8,16]
while True:
# sequence.append(2)
sequence.append(4)
result = sequence_inverter.invert_sequence(sequence, (0,1))
print(f"{len(sequence)}: {large_division(result, 100)}")
def test_sequence_inverter_on_normal():
for i in range(0, len(NORMAL_SEQUENCE), 250):
sequence = NORMAL_SEQUENCE[:i+1]
result = sequence_inverter.invert_sequence(sequence)
print(f"{len(sequence)}: {large_division(result, 100)}")
def sequence_7_trailing_bits():
sequence = [2,2,4,8,16]
values: list[tuple[int, int]] = []
binary_strings: list[str] = []
max_string_length = 0
for i in range(500):
sequence.append(4)
value = trailing_bit_generator.generate_trailing_bits(sequence, 1)
values.append(value)
binary_string = trailing_bit_generator.format_to_binary(value)
binary_strings.append(binary_string)
max_string_length = max(max_string_length, len(binary_string))
for i in range(len(sequence)):
binary_string = binary_strings[i]
print(f"{" "*(max_string_length - len(binary_string))}{binary_string}")
def sequence_5_looped_2_adic():
sequence = [16]
for i in range(50):
sequence.append(4)
loop_result = loop_formula.get_loop(sequence)
division_result = p_adics.division(loop_result[0], loop_result[1])
print(f"{p_adics.convert_bits_to_string(division_result[0])}")
def doubling_sequence_loop():
sequence = [2]
numeral = 4
while True:
increase = len(sequence)
for j in range(increase):
sequence.append(numeral)
result = loop_formula.get_loop(sequence)
print(f"{len(sequence)}: {large_division(result, 100)}")
numeral = 4 if numeral == 2 else 2
def fours_and_twos_loop():
for length in range(1, 1000, 10):
sequence: list[int] = []
for i in range(length):
sequence.append(4)
for i in range(length):
sequence.append(2)
result = loop_formula.get_loop(sequence)
print(f"{len(sequence)}: {large_division(result, 100)}")
if __name__ == "__main__":
fours_and_twos_loop()