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

Beatty's sequence of type 1.

1,3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,40,42,43,45,46,48,50,
51,53,55,56,58,59,61,63,64,66,67,69,71,72,74,76,77,79,80,82,84,85,87,88,90,92,93,95,97,
98,100,101,103,105,106,108,110,111,113,114,116,118,119,121,122,124,126,127,129,131,132,
134,135,137,139,140,142,144,145,147,148,150,152,153,155,156,158,160,161,...

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



shaft utilization:

    1:  25% +++++++++++++++++++++++++
    2:  24% ++++++++++++++++++++++++
    3:  24% ++++++++++++++++++++++++
    4:  27% +++++++++++++++++++++++++++

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



shaft utilization:

    1:  21% +++++++++++++++++++++
    2:  21% +++++++++++++++++++++
    3:  19% +++++++++++++++++++
    4:  19% +++++++++++++++++++
    5:  20% ++++++++++++++++++++

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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e-mail: ralph@cs.arizona.edu

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