#36 - Double-base palindromes

10 May 2016 in Project Euler on 5%

The decimal number, $585=1001001001_2$ (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

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Python has a convenient built-in function bin() that converts the number to binary. To check if a number is a palindrome, we will reverse and check for equality.

# file: "problem036.py"
s = 0
isPalindrome = lambda x: x == x[::-1]
for i in range(1, 1000000):
    if isPalindrome(str(i)) and isPalindrome(bin(i)[2:]):
        s += i
print(s)

The output of the code is,

872187
0.49978133307417255 seconds.

Thus, our needed sum is 872187.