Last modified Wednesday, April 11, 2001 1:09 pm

Farey sequence denominators.

4: 1 4 3 2 3 4 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++


5: 1 5 4 3 5 2 5 3 4 5 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++


6: 1 6 5 4 3 5 2 5 3 4 5 6 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++


7: 1 7 6 5 4 7 3 5 7 2 7 5 3 7 4 5 6 7 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++


8: 1 8 7 6 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 6 7 8 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++


9: 1 9 8 7 6 5 9 4 7 3 8 5 7 9 2 9 7 5 8 3 7 4 9 5 6 7 8 9 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++


10: 1 10 9 8 7 6 5 9 4 7 10 3 8 5 7 9 2 9 7 5 8 3 10 7 4 9 5 6 7 8 9 
10 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++


11: 1 11 10 9 8 7 6 11 5 9 4 11 7 10 3 11 8 5 7 9 11 2 11 9 7 5 8 11 3 
10 7 11 4 9 5 11 6 7 8 9 10 11 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++


12: 1 12 11 10 9 8 7 6 11 5 9 4 11 7 10 3 11 8 5 12 7 9 11 2 11 9 7 12 
5 8 11 3 10 7 11 4 9 5 11 6 7 8 9 10 11 12 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++


13: 1 13 12 11 10 9 8 7 13 6 11 5 9 13 4 11 7 10 13 3 11 8 13 5 12 7 9 
11 13 2 13 11 9 7 12 5 13 8 11 3 13 10 7 11 4 13 9 5 11 6 13 7 8 9 10 
11 12 13 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++


14: 1 14 13 12 11 10 9 8 7 13 6 11 5 14 9 13 4 11 7 10 13 3 14 11 8 13 
5 12 7 9 11 13 2 13 11 9 7 12 5 13 8 11 14 3 13 10 7 11 4 13 9 14 5 11 
6 13 7 8 9 10 11 12 13 14 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++


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



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++
   15:   8  ++++++++


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



shaft utilization:

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


17: 1 17 16 15 14 13 12 11 10 9 17 8 15 7 13 6 17 11 16 5 14 9 13 17 4 
15 11 7 17 10 13 16 3 17 14 11 8 13 5 17 12 7 16 9 11 13 15 17 2 17 15 
13 11 9 16 7 12 17 5 13 8 11 14 17 3 16 13 10 17 7 11 15 4 17 13 9 14 
5 16 11 17 6 13 7 15 8 17 9 10 11 12 13 14 15 16 17 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++
   15:   8  ++++++++
   16:   8  ++++++++
   17:  16  ++++++++++++++++


18: 1 18 17 16 15 14 13 12 11 10 9 17 8 15 7 13 6 17 11 16 5 14 9 13 
17 4 15 11 18 7 17 10 13 16 3 17 14 11 8 13 18 5 17 12 7 16 9 11 13 15 
17 2 17 15 13 11 9 16 7 12 17 5 18 13 8 11 14 17 3 16 13 10 17 7 18 11 
15 4 17 13 9 14 5 16 11 17 6 13 7 15 8 17 9 10 11 12 13 14 15 16 17 18 
1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++
   15:   8  ++++++++
   16:   8  ++++++++
   17:  16  ++++++++++++++++
   18:   6  ++++++


19: 1 19 18 17 16 15 14 13 12 11 10 19 9 17 8 15 7 13 19 6 17 11 16 5 
19 14 9 13 17 4 19 15 11 18 7 17 10 13 16 19 3 17 14 11 19 8 13 18 5 
17 12 19 7 16 9 11 13 15 17 19 2 19 17 15 13 11 9 16 7 19 12 17 5 18 
13 8 19 11 14 17 3 19 16 13 10 17 7 18 11 15 19 4 17 13 9 14 19 5 16 
11 17 6 19 13 7 15 8 17 9 19 10 11 12 13 14 15 16 17 18 19 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++
   15:   8  ++++++++
   16:   8  ++++++++
   17:  16  ++++++++++++++++
   18:   6  ++++++
   19:  18  ++++++++++++++++++


20: 1 20 19 18 17 16 15 14 13 12 11 10 19 9 17 8 15 7 20 13 19 6 17 11 
16 5 19 14 9 13 17 4 19 15 11 18 7 17 10 13 16 19 3 20 17 14 11 19 8 
13 18 5 17 12 19 7 16 9 20 11 13 15 17 19 2 19 17 15 13 11 20 9 16 7 
19 12 17 5 18 13 8 19 11 14 17 20 3 19 16 13 10 17 7 18 11 15 19 4 17 
13 9 14 19 5 16 11 17 6 19 13 20 7 15 8 17 9 19 10 11 12 13 14 15 16 
17 18 19 20 1 



shaft utilization:

    1:   2  ++
    2:   1  +
    3:   2  ++
    4:   2  ++
    5:   4  ++++
    6:   2  ++
    7:   6  ++++++
    8:   4  ++++
    9:   6  ++++++
   10:   4  ++++
   11:  10  ++++++++++
   12:   4  ++++
   13:  12  ++++++++++++
   14:   6  ++++++
   15:   8  ++++++++
   16:   8  ++++++++
   17:  16  ++++++++++++++++
   18:   6  ++++++
   19:  18  ++++++++++++++++++
   20:   8  ++++++++
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e-mail: ralph@cs.arizona.edu

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