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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.~~

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 <a class="badge is-tag">code-golf</a>. Shortest answer in every language wins.

code-golf sequence