variable definitions - How to define a vector with automatically added symbolic elements with subscripts

I want to define a vector lets say k containing elements Symbolize[Subscript[k, 1]], k2, k3 ... etc. When I define lets say k4 . I want the symbol automatically added to vector k. Something like below but not working at all.

k /: {k, Symbolize[

 ParsedBoxWrapper[
 SubscriptBox[
 StyleBox["v", FontFamily -> "Courier New", FontWeight -> "Plain", 
   FontSlant -> "Italic"], "_"]]]} := 
AppendTo[k, Subscript[v, _]];

My Question is;

1) How can I symbolically define elements (with sub scripts) automatically added to a vector.

2) If I assign values to symbols, How can I get elements values only and symbols only.

EDIT 1

Symbolize[Subscript[k, _]] 

Command Symbolizes all subscripts of k e.g. k1 (Subscript[k, 1]), k2 (Subscript[k, 2]) etc. This is fine. What I want is collect k1, k2 k3 in a set (List) k with out additional commands or additional functions. Just as soon as sybolize sub scripted ones it should add it self to set k (sort of pattern maching as in Subscript[k, _]). When I call k it should give me the list {k1, k2, k3}. @Mr. Wizards answer gives the list but as calling function ksym. Sort of what I need but not exactly. @halirutan answer is also interesting but I don' t want to define additional functions or operators (may be as minimum as possible).

EDIT 2

Its sort of bag or set; no order is required, only k1,k3 can be given and k2 can be missing.

EDIT 3

<< Notation`
(*below line symbolizes all subscripted k_]*)
Symbolize[ ParsedBoxWrapper[
   SubscriptBox["k", "_"]]]

somewhere here I need additional code that all k_ are added to k once its been defined. For example:

{Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]} = {1, 2, 3}

after that when I ask k it should give me {Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]} as @Mr.Wizard suggested ksym[] := HoldForm @@@ UpValues[k][[All, 1]] and for values kval[] := UpValues[k][[All, 2]] should work. But, what I' m missing in @Mr.Wizard example is that one needs to define symbols as;

k /: Subscript[k, 1] = "val1";
k /: Subscript[k, 2] = "val2";
k /: Subscript[k, 3] = "val3";

what I need is once I write {Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]} = {1, 2, 3} I should be able to get k vector and {Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]} is appended automatically to k.

Answer

Method #1

If you define each Subscript using TagSet⁽¹⁾⁽²⁾ the value will be associated with the Symbol, e.g. k:

k /: Subscript[k, 1] = "val1";
k /: Subscript[k, 2] = "val2";
k /: Subscript[k, 3] = "val3";

You could then use definitions such as:

kval[] := UpValues[k][[All, 2]]


ksym[] := HoldForm @@@ UpValues[k][[All, 1]]

These will always be up to date as they are dynamically generated:

kval[]

{"val1", "val2", "val3"}

ksym[]

{k₁, k₂, k₃}

Each "symbol" name is wrapped in HoldForm to prevent evaluation; ReleaseHold may be used to trigger it.

These definitions assume that no other UpValues for k are generated but if there are that can be addressed with pattern matching at the expense of speed.

---

Method #2

Following your update EDIT 3 here is another approach you might consider. Start by setting HoldFirst on Subscript so that k may be used without forming an infinite recursion, then make a definition for k that extracts the matching rules from the DownValues list:

SetAttributes[Subscript, HoldFirst]


k := Cases[DownValues@Subscript, (_[x : Subscript[k, _]] :> _) :> Hold[x]]

Make some assignments and check k:

{Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]} = {"a", "b", "c"}

k

{Hold[Subscript[k, 1]], Hold[Subscript[k, 2]], Hold[Subscript[k, 3]]}

The subscripts are returned in held form, for further processing. One can use ReleaseHold to recover the values:

k // ReleaseHold

{"a", "b", "c"}