perfect example of recycling vectors in R
# 1.
x = 1; y = 19; m1 = 2; m2 = 4
(x:y)[c(TRUE, rep(FALSE, m1-1), TRUE, rep(FALSE,m2-1))]
# [1] 1 3 7 9 13 15 19
# 2.
x = 3; y = 56; m1 = 7; m2 = 10
(x:y)[c(TRUE, rep(FALSE, m1-1), TRUE, rep(FALSE,m2-1))]
# [1] 3 10 20 27 37 44 54