Last modified Wednesday, April 11, 2001 1:27 pm

Beatty's sequence of type 2.

2,5,7,10,13,15,18,20,23,26,28,31,34,36,39,41,44,47,49,52,54,57,60,62,65,68,70,73,75,78,
81,83,86,89,91,94,96,99,102,104,107,109,112,115,117,120,123,125,128,130,133,136,138,141,
143,146,149,151,154,157,159,162,164,167,170,172,175,178,180,183,185,188,191,193,196,198,
201,204,206,209,212,214,217,219,222,225,227,230,233,235,238,240,243,246,248,251,253,256,
259,261,...

s=4:

no period detected

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



shaft utilization:

    1:  25% +++++++++++++++++++++++++
    2:  26% ++++++++++++++++++++++++++
    3:  26% ++++++++++++++++++++++++++
    4:  23% +++++++++++++++++++++++



s=5:

period = 21; pre-periodic length = 34

2,5,2,5,3,5,3,5,3,1,3,1,4,1,4,1,4,2,4,2,4,2,5,2,5,3,5,3,5,3,1,3,1,4,[1,4,1,4,2,4,2,4,2,5,
2,5,3,5,3,5,3,1,3,1,3] ...



shaft utilization:

    1:  20% ++++++++++++++++++++
    2:  18% ++++++++++++++++++
    3:  23% +++++++++++++++++++++++
    4:  19% +++++++++++++++++++
    5:  20% ++++++++++++++++++++



s=6:

no period detected

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



shaft utilization:

    1:  17% +++++++++++++++++
    2:  17% +++++++++++++++++
    3:  16% ++++++++++++++++
    4:  16% ++++++++++++++++
    5:  18% ++++++++++++++++++
    6:  16% ++++++++++++++++



s=7:

no period detected

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



shaft utilization:

    1:  13% +++++++++++++
    2:  16% ++++++++++++++++
    3:  15% +++++++++++++++
    4:  14% ++++++++++++++
    5:  15% +++++++++++++++
    6:  14% ++++++++++++++
    7:  13% +++++++++++++



s=8:

no period detected

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



shaft utilization:

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



s=9:

no period detected

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



shaft utilization:

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



s=10:

no period detected

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



shaft utilization:

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



s=11:

period = 21; pre-periodic length = 34

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



shaft utilization:

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



s=12:

no period detected

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



shaft utilization:

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



s=13:

no period detected

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



shaft utilization:

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



s=14:

no period detected

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



shaft utilization:

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



s=15:

no period detected

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



shaft utilization:

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



s=16:

no period detected

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



shaft utilization:

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

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