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.)

## Sage Solution

This is relatively straightforward in Sage.

import time def is_palindromic(n): d = n.digits() if len(d) == 1: return True for i in range(floor(len(d)/2)): if d[i] != d[len(d)-1-i]: return False return True def is_b_palindromic(n): n = ZZ(bin(n).split('0b')[1]) return is_palindromic(n) start = time.time() s = 0 for n in range(1000000): if is_palindromic(ZZ(n)) and is_b_palindromic(ZZ(n)): s += n elapsed = time.time() - start print "result %s found in %s seconds" % (s, elapsed)

Executing that bit of code, we get the following result.

result 872187 found in 21.3442850113 seconds