Generating ordered combination of numbers [closed]

I can form numbers with only 0,2,4,6,8.

The sequence is as follows 0,2,4,6,8,20,22,24,26,28,40,42,.....

How to generate an ordered sequence of numbers from combinations of 0,2,4,6,8.

Solution 1:

Divide each number by 2 and then imagine that the resulting digit patterns are in base 5 rather than base 10. What are the numbers then?

Sequence:

$0, 2, 4, 6 ,8, 20, 22, 24, ... $

Divide by 2:

$0, 1, 2, 3, 4, 10, 11, 12, ... $

Treat digital patterns as if they were base 5:

$0_5, 1_5, 2_5, 3_5, 4_5, 10_5, 11_5, 12_5, ...$

Translate base 5 numbers back to base 10:

$0, 1, 2, 3, 4, 5, 6, 7, ... $

Hmmm...

To find the 100th number in the sequence, work this pattern backwards:

$100-1=99$

$99=344_5$

$344_{10}×2=688$

This should just about do it.