TypeScript type for stringified values of a number union type

Question

I am trying to define a TypeScript type that restricts values to the string versions of a set of numbers. Explanation below:

Say I have a union numeric type like so:

const ONE = 1;
const TWO = 2;

type ALLOWED_NUMBER = typeof ONE | typeof TWO;

I would like to also define a companion string type that only allows the stringified versions of these numbers. So that I could do the following:

type ALLOWED_NUMBER_STRING = /* insert solution here :) */

const numericStringA: ALLOWED_NUMBER_STRING = '1';    // no error
const numericStringB: ALLOWED_NUMBER_STRING = '3';    // error
const numericStringC: ALLOWED_NUMBER_STRING = 'foo';  // error

I could manually define this type but it would be great to avoid the redundancy!