Why does n-of show a discontinuity when the size of the reported agentset goes from 2 to 3?

The n-of reporter is one of those reporters making random choices, so we know that if we use the same random-seed we will always get the same agentset out of n-of.

n-of takes two arguments: size and agentset (it can also take lists, but a note on this later). I would expect that it works by throwing a pseudo-random number, using this number to choose an agent from agentset, and repeating this process size times.

If this is true we would expect that, if we test n-of on the same agentset and using the same random-seed, but each time increasing size by 1, every resulting agentset will be the same as in the previous extraction plus a further agent. After all, the sequence of pseudo-random numbers used to pick the first (size - 1) agents was the same as before.

This seems to be confirmed generally. The code below highlights the same patches plus a further one everytime size is increased, as shown by the pictures:

to highlight-patches [n]
  clear-all
  random-seed 123
  
  resize-world -6 6 -6 6

  ask n-of n patches [
    set pcolor yellow
  ]
  
  ask patch 0 0 [
    set plabel word "n = " n
  ]
end

But there is an exception: the same does not happen when size goes from 2 to 3. As shown by the pictures below, n-of seems to follow the usual behaviour when starting from a size of 1, but the agentset suddenly changes when size reaches 3 (becoming the agentset of the figures above - which, as far as I can tell, does not change anymore):

What is going on there behind the scenes of n-of, that causes this change at this seemingly-unexplicable threshold?

In particular, this seems to be the case only for n-of. In fact, using a combination of repeat and one-of doesn't show this discontinuity (or at least as far as I've seen):

to highlight-patches-with-repeat [n]
  clear-all
  random-seed 123

  resize-world -6 6 -6 6
  
  repeat n [
    ask one-of patches [
      set pcolor yellow
    ]
  ]
  
  ask patch 0 0 [
    set plabel word "n = " n
  ]
end

Note that this comparison is not influenced by the fact that n-of guarantees the absence of repetitions while repeat + one-of may have repetitions (in my example above the first repetition happens when size reaches 13). The relevant aspect simply is that the reported agentset of size x is consistent with the reported agentset of size x + 1.

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On using n-of on lists instead of agentsets

Doing the same on a list results in always different numbers being extracted, i.e. the additional extraction does not equal the previous extraction with the addition of a further number. While this looks to me as a counter-intuitive behaviour from the point of view of expecting always the same items to be extracted from a list if the extraction is based on always the same sequence of pseudo-random numbers, at least it looks to happen consistently and therefore it does not look to me as ambiguous behaviour as in the case of agentsets.