Double-base Palindromes

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.)

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.