Quote from: kTimesG on May 05, 2024, 03:33:23 PM

are close to 0% of the total possible different patterns

Interestingly, the content of such numbers increases with the growth and height of the range.

Quote

============================= RESTART: D:\NumHex.py ============================
In the range from 0x1000 to 0x2000, 1 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.02% of the total hexadecimal numbers in the range.

============================= RESTART: D:\NumHex.py ============================
In the range from 0x10000 to 0x20000, 32 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.05% of the total hexadecimal numbers in the range.

============================= RESTART: D:\NumHex.py ============================
In the range from 0x100000 to 0x200000, 737 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.07% of the total hexadecimal numbers in the range.

============================= RESTART: D:\NumHex.py ============================
In the range from 0x1000000 to 0x2000000, 15617 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.09% of the total hexadecimal numbers in the range.

============================= RESTART: D:\NumHex.py ============================
In the range from 0x10000000 to 0x20000000, 311282 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.12% of the total hexadecimal numbers in the range.

============================= RESTART: D:\NumHex.py ============================
In the range from 0x100000000 to 0x200000000, 5963072 hexadecimal numbers were found with repeating digits occurring four or more times in a row.
This accounts for 0.14% of the total hexadecimal numbers in the range.

Anyone who wishes can calculate independently in the 130 range, but it will be a very long time:

Code:

def count_repeated_digits_hex(start, end):
count = 0
total_nums = int(end, 16) - int(start, 16) + 1

def has_repeated_digits(num_str):
prev_digit = None
consecutive_count = 0

for digit in num_str:
if digit == prev_digit:
consecutive_count += 1
else:
consecutive_count = 1

if consecutive_count >= 4:
return True

prev_digit = digit

return False

for num in range(int(start, 16), int(end, 16) + 1):
num_str = hex(num)[2:] # Remove '0x' prefix
if has_repeated_digits(num_str):
count += 1

percentage = (count / total_nums) * 100

return count, percentage

start = "0x100000000"
end = "0x200000000"
result, percentage = count_repeated_digits_hex(start, end)
print(f"In the range from {start} to {end}, {result} hexadecimal numbers were found with repeating digits occurring four or more times in a row.")
print(f"This accounts for {percentage:.2f}% of the total hexadecimal numbers in the range.")