What is an ES Number™?

Question

This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and the likewise inspired What is a Number™ series.

If a number conforms to a certain rule, I call it an ES Number™. Otherwise, I call it an OS Number™ Use the following examples to find the rule:

Here is a CSV:

ES Numbers™,OS Numbers™
4,5
96,48
343,434
2048,1024
15679,14679
86420,97531
1234567,6543210
543543543,210210210
3597175319,1354279860
8406268402,9068731254

The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is an ES Number™ or an OS Number™ on its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.

These are not the only examples of ES or OS Numbers™, more can be found.

EDIT: SORRY TO EVERYONE WHO ATTEMPTED THIS PUZZLE

I made a mistake in my ES Numbers™ list. 24 is actually an OS Number™. In order to make something similar to the original, I have included 96 which is an ES Number™. Unfortunately this makes the puzzle less cruel. ;)

Once again, sorry for the time you may or may not have wasted. I double-checked the puzzle and still didn't pick up the mistake. Now it is solvable in the intended way. (I've triple checked that)

Answer 1

An ES Number™ is a number that:

Uses an even number of segments when shown in a seven-segment display.

ES and OS stand for

Even-segmented and odd-segmented

Answer 2

I wonder whether ES numbers are simply those

whose digits have an even sum (hence ES).

There is a single obstacle to this, which is that

the digits of 48 add up to 12, which is even.

Is it possible that that one is a mistake?

Perhaps it was intended to be 12 (half the number in the ES column) rather than 48 (twice the number in the ES column).

Answer 3

Here's a solution, though if it's the intended one I'll be surprised.
Nevertheless, since it works to distinguish between the given ES and OS lists, I'll post it.

First let's assign ...

a PSEValue of 0 to the digits 1,4,6,9,0.
a PSEValue of 1 to the digits 2,3,5,7,8.

I don't have a particular justification for these PSEValues, other than the fact that these choices happen to make the pattern work, which is why I assume this isn't the actual solution.

Then we use that to find, for each number in the lists,

a sum of the PSEValues assigned to each digit in the number.

This gives us:

$$\begin{array}{|c|c|}\hline\Bbb{ES\ Numbers}^\text{TM}&\Bbb{OS\ Numbers}^\text{TM}\\\hline^{4: 0 → 0}&^{5: 1 → 1}\\^{96: 0+0 → 0}&^{48: 0+1 → 1}\\^{343: 1+0+1 → 2}&^{434: 0+1+0 → 1}\\^{2048: 1+0+0+1 → 2}&^{1024: 0+0+1+0 → 1}\\^{15679: 0+1+0+1+0 → 2}&^{14679: 0+0+0+1+0 → 1}\\^{86420: 1+0+0+1+0 → 2}&^{97531: 0+1+1+1+0 → 3}\\^{1234567: 0+1+1+0+1+0+1 → 4}&^{6543210: 0+1+0+1+1+0+0 → 3}\\^{543543543: 1+0+1+1+0+1+1+0+1 → 6}&^{210210210: 1+0+0+1+0+0+1+0+0 → 3}\\^{3597175319: 1+1+0+1+0+1+1+1+0+0 → 6}\ &^{1354279860: 0+1+1+0+1+1+0+1+0+0 → 5}\ \\^{8406268402: 1+0+0+0+1+0+1+0+0+1 → 4}\ &^{9068731254: 0+0+0+1+1+1+0+1+1+0 → 5}\ \\\hline\end{array}$$

So the numbers are called ES Numbers™ or OS Numbers™ depending on

whether the sum of the PSEValues for their digits is an Even Sum or an Odd Sum.

_{upgraded MagicValues to PSEValues, to fit the revised puzzle.}