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

signature sequence for pi.

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

s=4:

no period detected

1,2,3,4,1,1,2,2,3,3,4,1,4,1,2,1,2,3,2,3,4,1,3,4,1,2,4,1,2,3,1,2,3,4,1,2,3,4,1,2,3,4,1,2,
3,4,1,2,3,4,1,1,2,3,4,1,2,2,3,4,1,2,3,3,4,1,2,3,4,1,4,1,2,3,4,1,2,1,2,3,4,1,2,3,2,3,4,1,
2,3,4,1,3,4,1,2,3,4,1,2,...



shaft utilization:

    1:  28%  ++++++++++++++++++++++++++++
    2:  26%  ++++++++++++++++++++++++++
    3:  24%  ++++++++++++++++++++++++
    4:  22%  ++++++++++++++++++++++



s=5:

no period detected

1,2,3,4,1,5,2,1,3,2,4,1,3,5,2,4,1,3,5,2,4,1,1,3,5,2,2,4,1,3,3,5,2,4,1,4,1,3,5,2,5,2,4,1,
3,1,3,5,2,4,1,2,4,1,3,5,2,3,5,2,4,1,3,4,1,3,5,2,4,1,5,2,4,1,3,5,2,1,3,5,2,4,1,3,2,4,1,3,
5,2,4,1,3,5,2,4,1,3,5,2,...



shaft utilization:

    1:  23%  +++++++++++++++++++++++
    2:  22%  ++++++++++++++++++++++
    3:  20%  ++++++++++++++++++++
    4:  18%  ++++++++++++++++++
    5:  17%  +++++++++++++++++



s=6:

no period detected

1,2,3,4,1,5,2,6,3,1,4,1,2,5,2,3,6,3,4,1,4,1,5,2,5,2,6,3,6,3,1,4,1,4,1,2,5,2,5,2,3,6,3,6,
3,4,1,4,1,4,1,5,2,5,2,5,2,6,3,6,3,6,3,1,4,1,4,1,4,1,2,5,2,5,2,5,2,3,6,3,6,3,6,3,4,1,4,1,
4,1,4,1,5,2,5,2,5,2,5,2,...



shaft utilization:

    1:  20%  ++++++++++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  16%  ++++++++++++++++
    4:  16%  ++++++++++++++++
    5:  16%  ++++++++++++++++
    6:  12%  ++++++++++++



s=7:

no period detected

1,2,3,4,1,5,2,6,3,7,4,1,1,5,2,2,6,3,3,7,4,1,4,1,5,2,5,2,6,3,6,3,7,4,1,7,4,1,5,2,1,5,2,6,
3,2,6,3,7,4,1,3,7,4,1,5,2,4,1,5,2,6,3,5,2,6,3,7,4,1,6,3,7,4,1,5,2,7,4,1,5,2,6,3,1,5,2,6,
3,7,4,1,2,6,3,7,4,1,5,2,...



shaft utilization:

    1:  18%  ++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:  15%  +++++++++++++++
    4:  14%  ++++++++++++++
    5:  13%  +++++++++++++
    6:  12%  ++++++++++++
    7:  11%  +++++++++++



s=8:

no period detected

1,2,3,4,1,5,2,6,3,7,4,1,8,5,2,1,6,3,2,7,4,1,3,8,5,2,4,1,6,3,5,2,7,4,1,6,3,8,5,2,7,4,1,6,
3,8,5,2,7,4,1,1,6,3,8,5,2,2,7,4,1,6,3,3,8,5,2,7,4,1,4,1,6,3,8,5,2,5,2,7,4,1,6,3,6,3,8,5,
2,7,4,1,7,4,1,6,3,8,5,2,...



shaft utilization:

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



s=9:

no period detected

1,2,3,4,1,5,2,6,3,7,4,1,8,5,2,9,6,3,1,7,4,1,2,8,5,2,3,9,6,3,4,1,7,4,1,5,2,8,5,2,6,3,9,6,
3,7,4,1,7,4,1,8,5,2,8,5,2,9,6,3,9,6,3,1,7,4,1,7,4,1,2,8,5,2,8,5,2,3,9,6,3,9,6,3,4,1,7,4,
1,7,4,1,5,2,8,5,2,8,5,2,...



shaft utilization:

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



s=10:

no period detected

1,2,3,4,1,5,2,6,3,7,4,1,8,5,2,9,6,3,10,7,4,1,1,8,5,2,2,9,6,3,3,10,7,4,1,4,1,8,5,2,5,2,9,
6,3,6,3,10,7,4,1,7,4,1,8,5,2,8,5,2,9,6,3,9,6,3,10,7,4,1,10,7,4,1,8,5,2,1,8,5,2,9,6,3,2,9,
6,3,10,7,4,1,3,10,7,4,1,8,5,2,...



shaft utilization:

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



s=11:

no period detected

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



shaft utilization:

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



s=12:

no period detected

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



shaft utilization:

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



s=13:

no period detected

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



shaft utilization:

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



s=14:

no period detected

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



shaft utilization:

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



s=15:

no period detected

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



shaft utilization:

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



s=16:

no period detected

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



shaft utilization:

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

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