Start a week from given day and get week number in R

Lets have a sequence of dates,

df  = data.frame(date = seq(as.Date('2022-01-01'),as.Date('2022-01-31'),by = 1))

I want to start the week from Tuesday and then cut the dates to create new column week giving the week number. Required output is,

date           week
1  2022-01-01    1
2  2022-01-02    1
3  2022-01-03    1
4  2022-01-04    2
5  2022-01-05    2

Similarly, if I wanted to start the week from Wednesday the expected output is,

date           week
1  2022-01-01    1
2  2022-01-02    1
3  2022-01-03    1
4  2022-01-04    1
5  2022-01-05    2
6  2022-01-06    2

How can I get this done?

If the week were to start from Monday I would have used,

df%>% mutate(week = cut.Date(df$date, breaks = "1 week", labels = FALSE)) 
        date week
1  2022-01-01    1
2  2022-01-02    1
3  2022-01-03    2
4  2022-01-04    2
5  2022-01-05    2

Thank you for any help...

We may specify the week_start in floor_date (week_start - 1 would be Monday and 7 would be Sunday)

f1 <- function(dates, wk_start = 1) {
    new <- lubridate::floor_date(dates, 'week', week_start = wk_start)
    match(new, unique(new))
}

-checking

> library(dplyr)
> df %>%
+    mutate(week = f1(date, wk_start = 1)) %>%
+    head
        date week
1 2022-01-01    1
2 2022-01-02    1
3 2022-01-03    2
4 2022-01-04    2
5 2022-01-05    2
6 2022-01-06    2
> df %>%
+    mutate(week = f1(date, wk_start = 2)) %>%
+    head
        date week
1 2022-01-01    1
2 2022-01-02    1
3 2022-01-03    1
4 2022-01-04    2
5 2022-01-05    2
6 2022-01-06    2
> df %>%
+    mutate(week = f1(date, wk_start = 3)) %>%
+    head
        date week
1 2022-01-01    1
2 2022-01-02    1
3 2022-01-03    1
4 2022-01-04    1
5 2022-01-05    2
6 2022-01-06    2