Code Golf
liek
## 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.
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?

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