week("2000-01-01")
week("2000-01-06")
week("2000-01-07")
week("2000-01-13")
week("2000-01-14")

require(lubridate)
dates <- c("2000-01-01","2000-01-06","2000-01-07","2000-01-13","2000-01-14")
sapply(dates, isoweek)
2000-01-01 2000-01-06 2000-01-07 2000-01-13 2000-01-14
        52          1          1          2          2

require(lubridate)
my_week <- function(x){
  # fst monday of the same year
  first_sun <- as.POSIXct(paste0(year(x),"-01-Mon"), format = "%Y-%U-%a")
  (yday(x) + (7 - yday(first_sun) + 1)) %/% 7
}

dates <- seq(as.Date("2000-01-01"), as.Date("2000-01-15"), by=1)
a <- sapply(dates, my_week)
names(a) <- dates

> a
2000-01-01 2000-01-02 2000-01-03 2000-01-04 2000-01-05
         0          1          1          1          1
2000-01-06 2000-01-07 2000-01-08 2000-01-09 2000-01-10
         1          1          1          2          2
2000-01-11 2000-01-12 2000-01-13 2000-01-14 2000-01-15
         2          2          2          2          2