R - create vector with sequence c(1,4,5,8,9,12,13,16),etc

Question

We are looking to create a vector with the following sequence:

1,4,5,8,9,12,13,16,17,20,21,...

Start with 1, then skip 2 numbers, then add 2 numbers, then skip 2 numbers, etc., not going above 2000. We also need the inverse sequence 2,3,6,7,10,11,...

Answer 1

We may use recyling vector to filter the sequence

(1:21)[c(TRUE, FALSE, FALSE, TRUE)]
 [1]  1  4  5  8  9 12 13 16 17 20 21

Answer 2

Here's an approach using rep and cumsum. Effectively, "add up alternating increments of 1 (successive #s) and 3 (skip two)."

cumsum(rep(c(1,3), 500))

and

cumsum(rep(c(3,1), 500)) - 1

Answer 3

Got this one myself - head(sort(c(seq(1, 2000, 4), seq(4, 2000, 4))), 20)