some_dates <- as.POSIXct(c("2015-12-24", "2015-12-31", "2016-01-01", "2016-01-08"))

(year_week <- format(some_dates, "%Y-%U"))
## [1] "2015-51" "2015-52" "2016-00" "2016-01"
(year_week_day <- sprintf("%s-1", year_week))
## [1] "2015-51-1" "2015-52-1" "2016-00-1" "2016-01-1"
(as.POSIXct(year_week_day, format = "%Y-%U-%u"))
## [1] "2015-12-21 EST" "2015-12-28 EST" "2016-01-04 EST" "2016-01-04 EST"