Tournament bracket placement algorithm

Question

Given a list of opponent seeds (for example seeds 1 to 16), I'm trying to write an algorithm that will result in the top seed playing the lowest seed in that round, the 2nd seed playing the 2nd-lowest seed, etc.

Grouping 1 and 16, 2 and 15, etc. into "matches" is fairly easy, but I also need to make sure that the higher seed will play the lower seed in subsequent rounds.

An example bracket with the correct placement:

1 vs 16
            1 vs 8
8 vs 9
                        1 vs 4
4 vs 13
            4 vs 5
5 vs 12
                                    1 vs 2
2 vs 15
            2 vs 7
7 vs 10
                        2 vs 3
3 vs 14
            3 vs 6
6 vs 11

As you can see, seed 1 and 2 only meet up in the final.

Answer 1

This JavaScript returns an array where each even index plays the next odd index

function seeding(numPlayers){
  var rounds = Math.log(numPlayers)/Math.log(2)-1;
  var pls = [1,2];
  for(var i=0;i<rounds;i++){
    pls = nextLayer(pls);
  }
  return pls;
  function nextLayer(pls){
    var out=[];
    var length = pls.length*2+1;
    pls.forEach(function(d){
      out.push(d);
      out.push(length-d);
    });
    return out;
  }
}

> seeding(2)
[1, 2]
> seeding(4)
[1, 4, 2, 3]
> seeding(8)
[1, 8, 4, 5, 2, 7, 3, 6]
> seeding(16)
[1, 16, 8, 9, 4, 13, 5, 12, 2, 15, 7, 10, 3, 14, 6, 11]