Symbols for "odd" and "even"

Question

Let $A$ be a sequence of letters $\langle a,b,c,d,e,f \rangle$. I want to create two subsequences, one with the values with odd index and other with the values with even index: $A_\mathrm{odd} = \langle a,c,e \rangle$ and $A_\mathrm{even} = \langle b,d,f \rangle$.

My question is: is there any usual symbol that could substitute the words "odd" and "even" in the name of the subsequence?

Thanks!

Answer 1

The best I can come up with is $A_{2k+1}$ and $A_{2k}$.

Answer 2

How about $A_\mathcal O$ and $A_\mathcal E$?

To produce these: A_\mathcal O and A_\mathcal E

Answer 3

"odd" and "even" are fine. Maybe in roman not italic, though: $$ A_{\rm{odd}} \ne A_{\rm{even}} $$ since the first subscript is not a product $odd$ of three factors.

Answer 4

To say that $x$ is even is to say that $x\equiv 0 \bmod 2$ and to say that it is odd is to say that $x\equiv 1 \bmod 2$. So you could use $A_0$ and $A_1$.

But, to be honest, I prefer $A_{\mathrm{e}}$ and $A_{\mathrm{o}}$, since they're as easy to remember as $A_{\mathrm{even}}$ and $A_{\mathrm{odd}}$ but more concise.

Answer 5

We could write even number symbol as it’s abbreviation, that is e-n. Similarly for odd number, we could write o-n.