Last modified Sunday, July 16, 2000 12:23 pm

signature sequence for sqrt(2).

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

s=4:
no period detected 1,2,1,3,2,1,4,3,2,1,1,4,3,2,2,1,1,4,3,3,2,2,1,4,1,4,3,3,2,1,2,1,4,1,4,3,2,3,2,1,2,1,4,1, 3,4,3,2,3,2,1,2,4,1,4,1,3,4,3,2,3,1,2,1,2,4,1,4,1,3,4,2,3,2,3,1,2,1,2,4,1,3,4,1,3,4,2,3, 2,3,1,2,4,1,2,4,1,3,4,1,...



shaft utilization:

    1:  30%  ++++++++++++++++++++++++++++++
    2:  26%  ++++++++++++++++++++++++++
    3:  23%  +++++++++++++++++++++++
    4:  21%  +++++++++++++++++++++

s=5:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,1,2,5,1,4,2,3,1,2,5,3,1,4,2,3,1,4,2,5,3,1,4,2,5,3,1,4,2,5,3,1, 1,4,2,5,3,1,4,2,2,5,3,1,1,4,2,5,3,3,1,4,2,2,5,3,1,1,4,4,2,5,3,3,1,4,2,2,5,5,3,1,1,4,4,2, 5,3,3,1,1,4,2,2,5,5,3,1,...



shaft utilization:

    1:  25%  +++++++++++++++++++++++++
    2:  22%  ++++++++++++++++++++++
    3:  20%  ++++++++++++++++++++
    4:  17%  +++++++++++++++++
    5:  16%  ++++++++++++++++

s=6:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,1,3,6,2,5,2,1,4,1,3,6,3,2,5,2,1,4,1,4,3,6,3,2,5,2,1, 5,4,1,4,3,6,3,2,6,5,2,1,5,4,1,4,3,1,6,3,2,6,5,2,1,5,4,2,1,4,3,1,6,3,2,6,5,3,2,1,5,4,2,1, 4,3,1,6,4,3,2,6,5,3,2,1,...



shaft utilization:

    1:  22%  ++++++++++++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  18%  ++++++++++++++++++
    4:  15%  +++++++++++++++
    5:  13%  +++++++++++++
    6:  12%  ++++++++++++

s=7:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,1,1,4,7,3,6,2,2,5,1,1,4,7,3,3,6,2,2,5,1,1, 4,4,7,3,3,6,2,2,5,5,1,1,4,4,7,3,3,6,6,2,2,5,5,1,1,4,4,7,7,3,3,6,6,2,2,5,5,1,1,1,4,4,7,7, 3,3,6,6,2,2,2,5,5,1,1,1,...



shaft utilization:

    1:  21%  +++++++++++++++++++++
    2:  18%  ++++++++++++++++++
    3:  15%  +++++++++++++++
    4:  13%  +++++++++++++
    5:  13%  +++++++++++++
    6:  11%  +++++++++++
    7:   9%  +++++++++

s=8:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,1,2,5,8,1,4,7,2,3,6,1,2,5,8,1, 3,4,7,2,3,6,1,2,4,5,8,1,3,4,7,2,3,5,6,1,2,4,5,8,1,3,4,6,7,2,3,5,6,1,2,4,5,7,8,1,3,4,6,7, 2,3,5,6,8,1,2,4,5,7,8,1,...



shaft utilization:

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

s=9:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,1,3,6,9,2,5,8,1, 2,4,7,1,3,6,9,2,3,5,8,1,2,4,7,1,3,4,6,9,2,3,5,8,1,2,4,5,7,1,3,4,6,9,2,3,5,6,8,1,2,4,5,7, 1,3,4,6,7,9,2,3,5,6,8,1,...



shaft utilization:

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

s=10:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 1,4,7,10,3,6,9,2,2,5,8,1,1,4,7,10,3,3,6,9,2,2,5,8,1,1,4,4,7,10,3,3,6,9,2,2,5,5,8,1,1,4,4, 7,10,3,3,6,6,9,2,2,5,5,8,1,...



shaft utilization:

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

s=11:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,1,5,8,1,11,4,7,10,3,2,6,9,2,1,5,8,1,11,4,3,7,10,3,2,6,9,2,1,5,4,8,1,11, 4,3,7,10,3,2,6,5,9,2,1,5,4,8,1,...



shaft utilization:

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

s=12:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,12,5,8,1,11,4,7,10,3,1,6,9,2,12,5,8,1,11,4,2,7,10,3,1,6,9,2,12,5,3,8,1, 11,4,2,7,10,3,1,6,4,9,2,12,5,3,8,1,...



shaft utilization:

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

s=13:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,12,5,8,1,11,4,7,10,3,13,6,9,2,12,5,8,1,11,4,1,7,10,3,13,6,9,2,12,5,2,8, 1,11,4,1,7,10,3,13,6,3,9,2,12,5,2,8,1,...



shaft utilization:

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

s=14:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,12,5,8,1,11,4,7,10,3,13,6,9,2,12,5,8,1,11,4,14,7,10,3,13,6,9,2,12,5,1, 8,1,11,4,14,7,10,3,13,6,2,9,2,12,5,1,8,1,...



shaft utilization:

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

s=15:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,12,5,8,1,11,4,7,10,3,13,6,9,2,12,5,8,1,11,4,14,7,10,3,13,6,9,2,12,5,15, 8,1,11,4,14,7,10,3,13,6,1,9,2,12,5,15,8,1,...



shaft utilization:

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

s=16:
no period detected 1,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,8,1,4,7,3,6,9,2,5,8,1,4,7,10,3,6,9,2,5,8,1, 11,4,7,10,3,6,9,2,12,5,8,1,11,4,7,10,3,13,6,9,2,12,5,8,1,11,4,14,7,10,3,13,6,9,2,12,5,15, 8,1,11,4,14,7,10,3,13,6,16,9,2,12,5,15,8,1,...



shaft utilization:

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

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e-mail: ralph@cs.arizona.edu

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