How to sum up in two vector without overriding the results

I would like to sum up two vectors, in a way that:

A = seq(10, 30, 10)
B = seq(1, 6, 1)
C = c()

for (i in B) {
  for (j in A)
  C = c(j + i)
}

C would be a vector with all results appearing from:

for (i in B) {
  for (j in A)
  print(j + i)
}

I am not interested in a matrix for this. What could I possibly do?
Thanks

You can use outer in this case.

c(outer(A, B, `+`))
[1] 11 21 31 12 22 32 13 23 33 14 24 34 15 25 35 16 26 36

If you really need a for loop, we can use the approach provided by @Feel free in the comment:

for (i in B) {
  for (j in A)
    C = append(C, j + i)
}

C
[1] 11 21 31 12 22 32 13 23 33 14 24 34 15 25 35 16 26 36

Dev solutions