Existing Roll and Round Function?

[applesauce]

I was wondering if there is an existing function that can (succinctly) accomplish the following. I'd like to group a column so each group's values are within a certain number (increment_var) of each other; for example, if increment_var is 4, then 1, 4, 7, 9 would group into (1, 4) and (7, 9). I wrote a for-loop below that emulates what the function would do. It sort of has the feel of DescTool's RoundTo and zoo's rollapply functions. Many thanks!

new_cars <- arrange(mtcars, mpg)

increment_var <- 5
counting_var <- 0
saved_var <- 0
for (i in 1:nrow(new_cars)){
  trial_var <- new_cars[i, "mpg"]
  if (trial_var - saved_var > increment_var){
    counting_var = counting_var + 1
    saved_var = trial_var
  }
  new_cars[i, "new_col"] = counting_var
}

select(new_cars, c(mpg, new_col))
#   mpg new_col
# 1  10.4       1
# 2  10.4       1
# 3  13.3       1
# 4  14.3       1
# 5  14.7       1
# 6  15.0       1
# 7  15.2       1
# 8  15.2       1
# 9  15.5       2
# 10 15.8       2
# 11 16.4       2
# 12 17.3       2
# 13 17.8       2
# 14 18.1       2
# 15 18.7       2
# 16 19.2       2
# 17 19.2       2
# 18 19.7       2
# 19 21.0       3
# 20 21.0       3
# 21 21.4       3
# 22 21.4       3
# 23 21.5       3
# 24 22.8       3
# 25 22.8       3
# 26 24.4       3
# 27 26.0       3
# 28 27.3       4
# 29 30.4       4
# 30 30.4       4
# 31 32.4       5
# 32 33.9       5