How would I efficiently go about taking a 1-by-1 ascending random sample of the values 1:n, making sure that each of the randomly sampled values is always higher than the previous value?

e.g.:

For the values 1:100, get a random number, say which is 61. (current list=61)
Then pick another number between 62 and 100, say which is 90 (current list=61,90)
Then pick another number between 91 and 100, say which is 100.
Stop the process as the max value has been hit (final list=61,90,100)

I have been stuck in loop land, thinking in this clunky manner:

a1 <- sample(1:100,1)

if(a1 < 100) {
    a2 <- sample((a+1):100,1)
        }

etc etc...

I want to report a final vector being the concatenation of a1,a2,a(n):

result <- c(a1,a2)

Even though this sounds like a homework question, it is not. I thankfully left the days of homework many years ago.

r random sample
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