Last modified Wednesday, December 15, 1999 5:36 pm

Connell's sequence.

1,2,4,5,7,9,10,12,14,16,17,19,21,23,25,26,28,30,32,34,36,37,39,41,43,45,47,49,50,52,54,
56,58,60,62,64,65,67,69,71,73,75,77,79,81,82,84,86,88,90,92,94,96,98,100,101,103,105,107,
109,111,113,115,117,119,121,122,124,126,128,130,132,134,136,138,140,142,144,145,147,149,
151,153,155,157,159,161,163,165,167,169,170,172,174,176,178,180,182,184,186,...

s=4:

no period detected

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



shaft utilization:

    1:  28%  ++++++++++++++++++++++++++++
    2:  26%  ++++++++++++++++++++++++++
    3:  21%  +++++++++++++++++++++
    4:  25%  +++++++++++++++++++++++++



s=5:

no period detected

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



shaft utilization:

    1:  20%  ++++++++++++++++++++
    2:  23%  +++++++++++++++++++++++
    3:  14%  ++++++++++++++
    4:  23%  +++++++++++++++++++++++
    5:  20%  ++++++++++++++++++++



s=6:

no period detected

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



shaft utilization:

    1:  19%  +++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:  14%  ++++++++++++++
    4:  19%  +++++++++++++++++++
    5:  16%  ++++++++++++++++
    6:  15%  +++++++++++++++



s=7:

no period detected

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



shaft utilization:

    1:  12%  ++++++++++++
    2:  19%  +++++++++++++++++++
    3:  12%  ++++++++++++
    4:  15%  +++++++++++++++
    5:  16%  ++++++++++++++++
    6:  10%  ++++++++++
    7:  16%  ++++++++++++++++



s=8:

no period detected

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



shaft utilization:

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



s=9:

no period detected

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



shaft utilization:

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



s=10:

no period detected

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



shaft utilization:

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



s=11:

no period detected

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



shaft utilization:

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



s=12:

no period detected

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



shaft utilization:

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



s=13:

no period detected

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



shaft utilization:

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



s=14:

no period detected

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



shaft utilization:

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



s=15:

no period detected

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



shaft utilization:

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



s=16:

no period detected

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



shaft utilization:

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

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