##Introduction

Inspired by the very recent video The Trapped Knight - Numberphile, I came up with a challenge.

The trapped knight sequence is a finite integer sequence of length 2016, starting from 1, and has the following construction rules:

1. Write a number spiral in the following manner:

17 16 15 14 13 ...
18  5  4  3 12 ...
19  6  1  2 11 ...
20  7  8  9 10 ...
21 22 23 24 25 ...

2. Place a knight on 1.
3. Move the knight to the grid with the smallest number it can go that has not been visited before, according to the rules of chess (i.e. 2 units vertically and 1 unit horizontally, or vice versa).
4. Repeat until the knight gets stuck.

Here is the first three steps:

Step 1

 17  [16]  15  [14]  13 
[18]   5    4    3  [12]
 19    6  < 1>   2   11 
[20]   7    8    9  [10]
 21  [22]  23  [24]  25 

Possible moves are 10, 12, 14, 16, 18, 20, 22, 24, among which the smallest is 10, so the second term is 10.

Step 2

  4  [ 3]  12  [29]  54
( 1)   2   11   28  [53] 
  8    9  <10>  27   52 
[23]  24   25   26  [51] 
 46  [47]  48  [49]  50 

Possible moves are 1, 3, 23, 29, 47, 49, 51, 53, among which the smallest is 3, so the third term is 3.

Step 3

 35  [34]  33  [32]  31 
[16]  15   14   13  [30] 
  5    4  < 3>  12   29 
[ 6] ( 1)   2   11  [28] 
  7  [ 8]   9  (10)  27 

Possible moves are 6, 8, 10, 16, 28, 30, 32, 34, among which the smallest is 6, so the fourth term is 6.

The sequence stars with:

1 10 3 6 9 4 7 2 5 8 11 14 ...

and ends with

... 2099 2284 2477 2096 2281 2474 2675 2884 3101 2880 2467 2084

##Challenge

Write a shortest program or function, receiving an integer in the range [1, 2016] (or [0, 2015] if 0-indexed is used) as input, output the number at that index in the trapped knight sequence. You can choose to index the sequence with 0-indexed or 1-indexed, but you must specify which indexing scheme you use.

##Test cases (1-indexed)

n    | s(n)
-----+-----
   1 |    1
   2 |   10
   3 |    3
   6 |    4
  11 |   11
  21 |   23
  51 |   95
 101 |   65
 201 |  235
 501 |  761
1001 | 1069
2001 | 1925
2016 | 2084

For all possible outputs, please refer to this page.

##Winning Criteria

The shortest code of each language wins. Restrictions on standard loopholes apply.