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The Ludic Numbers

The Ludic Numbers

The Ludic Numbers are a sequence that pops up when you apply the sieve of eratosthenes to the natural numbers, completely removing the numbers every iteration.

Here is how they are generated:

The Ludic numbers start with the lists:
```
l = [1]
n = [2,3,4,5,6,7,8,9,10....]
```

Every iteration, we take the first element `x` in `n`, add it to the list, and remove every `x`th number in `n`, including `x`.

```
l = [1,2]
n = [3,5,7,9,11,...]
```

By repeating this process an infinite number of times, we can get the full list of Ludic numbers.

# Challenge
For this sequence, you can
*    Take an index \$n\$ and output the \$n^{th}\$ term, either 0 or 1 indexed.
*    Take a positive integer \$n\$ and output the first \$n\$ terms.
*    Output the whole sequence as an infinite list.

# Testcases
```
1		1
2		2
3		3
4		5
5		7
6		11
7		13
8		17
9		23
10		25
11		29
12		37
13		41
14		43
15		47
16		53
```

The first 56 values can be seen here: [A003309](http://oeis.org/A003309/list).

Reference implementations can be found at [Rosetta Code](https://rosettacode.org/wiki/Ludic_numbers).

# Scoring
This is code-golf. Shortest answer in every language wins.