In R you can use either integers or a logical vector as an index (or a character vector for named access).
Your problem can be solved using either; for instance, you can generate an integer vector of the numbers 7, 14, … using seq:
index = seq(7L, length(x), by = 7L)
Or you can generate a logical vector that’s TRUE if and only if the corresponding integer index is divisible by 7:
index = seq_along(x) %% 7L == 0L
Either way, you then use that index to subset your data:
x[index]
Or, if you want to retain the other values but “empty” them (what does “empty” mean, though?) you can assign an empty value to them:
x[! index] = NA_character_ # or "", or something else.