Last modified Monday, April 23, 2001 8:47 am

Farey sequence numerators (each term incremented by 1 to give 1-based sequence).

4: 1 2 2 2 3 4 2 


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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


shaft utilization:

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


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e-mail: ralph@cs.arizona.edu

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