[1970-01-01]

You assumed this out of air.

"Powers of 2" means this:

Here are the powers of 2 from \( 2^{-11} \) to \( 2^{11} \) in a table format:

     | Power of 2   | Value              |
     |--------------|--------------------|
     | \( 2^{-11} \) | 0.00048828125      |
     | \( 2^{-10} \) | 0.0009765625       |
     | \( 2^{-9} \)  | 0.001953125        |
     | \( 2^{-8} \)  | 0.00390625         |
     | \( 2^{-7} \)  | 0.0078125          |
     | \( 2^{-6} \)  | 0.015625           |
     | \( 2^{-5} \)  | 0.03125            |
     | \( 2^{-4} \)  | 0.0625             |
     | \( 2^{-3} \)  | 0.125              |
     | \( 2^{-2} \)  | 0.25               |
     | \( 2^{-1} \)  | 0.5                |
     | \( 2^{0} \)   | 1                  |
     | \( 2^{1} \)   | 2                  |
     | \( 2^{2} \)   | 4                  |
     | \( 2^{3} \)   | 8                  |
     | \( 2^{4} \)   | 16                 |
     | \( 2^{5} \)   | 32                 |
     | \( 2^{6} \)   | 64                 |
     | \( 2^{7} \)   | 128                |
     | \( 2^{8} \)   | 256                |
     | \( 2^{9} \)   | 512                |
     | \( 2^{10} \)  | 1024               |
     | \( 2^{11} \)  | 2048               |

The evens include "0"

[andrewla]

??

This does not clarify -- your initial post made a claim about 0^2, which (correctly) does not appear in this list.

Moreover it is trivial that there are no negative powers of 2 that have all even digits, since the trailing digit will always be 5. So the question reduces to whether there are powers of 2 greater than 2048 that have all even digits.

[thehappypm]

0 is not in the “Value” column