# Function to check if a number is a palindrome in a given base
def is_palindrome(num: int, base: int) -> bool:
if base < 2:
return False # Invalid base
strnum_reversed = []
temp = num
# Convert number to string in given base
while temp > 0:
digit = temp % base
strnum_reversed.append(chr(ord('0') + digit) if digit < 10 else chr(ord('A') + (digit - 10)))
temp //= base
# Check palindrome
return strnum_reversed == strnum_reversed[::-1]
limit = 1000
print("Numbers that are palindromes in both base 10 and base 2:")
for i in range(1, limit + 1):
if is_palindrome(i, 10) and is_palindrome(i, 2):
print(f"{i} (binary: ", end='')
# Print binary representation
binary = []
temp = i
while temp > 0:
binary.append('1' if temp % 2 else '0')
temp //= 2
binary_str = ''.join(reversed(binary))
print(f"{binary_str})")
"""
run:
Numbers that are palindromes in both base 10 and base 2:
1 (binary: 1)
3 (binary: 11)
5 (binary: 101)
7 (binary: 111)
9 (binary: 1001)
33 (binary: 100001)
99 (binary: 1100011)
313 (binary: 100111001)
585 (binary: 1001001001)
717 (binary: 1011001101)
"""
