Why are you looping again inside? for(i in seq(from=1, to=10, by=1)){ i will be a straight sequence from 1 to 10 for(j in seq(from=1, to=2, by=1)){ j will only assume either 1 or 2 so:
if i=1 enters the first loop and j=1 the output[1,] <- 1
now j=2 and output[1,] <- 1
if what you want is to repeat the first value, your second assign should be the j value, something like this
output1 <- data.frame(matrix(ncol=1, nrow=10))
 colnames(output1) <- "id"
 for(i in seq(from=1, to=10, by=2)){
  for(j in seq(from=1, to=2, by=1)){
    output[i,] <- i
    output[i+1,] <- j
    print(paste(i))
  }
}
There are also better ways to achive your result (if repeating the value is your desired result)
output1 <- data.frame(matrix(ncol=1, nrow=10))
 colnames(output1) <- "id"
 for(i in seq(from=1, to=10, by=2)){
    output[i,] <- i
    output[i+1,] <- i+1
    print(paste(i))
}
you can also refer to this question Sequence of Repeated Values in R
which will basically tell you you can create a vector of repeated values in a sequence by using the rep() command in R