We can use lubridate, wdayto check if this is Monday, and dayto check if this is the first week of the month:
library(lubridate)
x <- seq(ymd("2010-01-01"),ymd("2015-12-31"),by="1 day")
x[wday(x,label = TRUE) == "Mon" & day(x) <= 7]
or in database-r (comment by @DavidArenburg)
x <- seq(as.Date("2010-01-01"), as.Date("2015-12-31"), by = "day")
x[weekdays(x) == "Monday" & as.numeric(format(x, "%d")) <= 7]
(five first results)
[1] "2010-01-04 UTC" "2010-02-01 UTC" "2010-03-01 UTC" "2010-04-05 UTC" "2010-05-03 UTC" "2010-06-07 UTC"
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