## Square Deltas
Given an *strictly* positive integer `n`, output all numbers in the sequence after the index `n`. For this specific challenge numbers are one-indexed.
## Base sequence
We start from this sequence:
```
1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, ...
```
The sequence is described as follows: `1, 2 (xN), 1` repeated arbitary times. There are 2 more `2`'s than the previous 2-set, and the 2-sequence starts at 1. i.e.:
```
1,       2,       1,
1,    2, 2, 2,    1,
1, 2, 2, 2, 2, 2, 1,
and so on ...
```

However, our point is not to output this sequence. For every item in this sequence, add the item by that item of that sequence.
## Adding the sequence
Here's an example of adding the sequence. Here, our sequence starts with 0:
```
  The sequence
    |
    v
0 + 1 = 1
1 + 2 = 3
3 + 1 = 4
4 + 1 = 5
...

Our generated sequence is therefore

0, 1, 3, 4, ...

```
## Example test cases
[Here](https://tio.run/##XVHLbsIwELznK1xONgRawqWKyl9U6iGKqghvhCV3HRwHwtenu3ZSUH3Zx6xnxuvuHs4OD9OkoRXtu@zhospM0OkBUBwpBKliw0MYPIpqFK3zYhQGCbwI01KOLqSa7jSoY83FrtFajqrOMuaHq7NXkM7qHOE268y01KgsIIOqpPk@ND58mXAmD3BtrDTYDWRFbfeZGwJ1qzozFKi0muJbdsIQY4CfLuG3s7EgPv0ASYsvbggxuTTrdbHdq9fX4jnf7OtlcNc7vzw9CdJ6KEmd4O@Jkk@SYbAiD8SxndNafRweY3zY44ZNcwHjCbrwGOiavk96Vn/Pr@BQ/S2jTPYiRjQsQ7MlS0VAm7YFD3iCuLZl3ZEs/0@VXkL/93Trhff25MgbDHL9GMgB9XElVmrxSTqknpjYUjFNxS8) is a sample program outputting the sequence starting from the input.
```
1 -> 0, 1, 3, 4, 5, 7, 9, 11, 12, 13, ...
4 -> 4, 5, 7, 9, 11, 12, 13, ...
```
## Rules
* The separator for the sequence can be any one-character string. It has to be consistent, i.e. you shouldn't use one space as a separator in one place and use two spaces in another place.
* The separator cannot be a digit or the null string.
* The sequence output system is intentionally designed to be an infinite sequence.

## Sandbox
* Is there a better name for this challenge?
* Can the challenge be clarified?
* Can this challenge be shorter?