Last modified Tuesday, January 11, 2000 5:03 pm

The positive integers.

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,...

s=4:
period = 4; pre-periodic length = 0 [1,2,3,4] ...



shaft utilization:

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

s=5:
period = 5; pre-periodic length = 0 [1,2,3,4,5] ...



shaft utilization:

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

s=6:
period = 6; pre-periodic length = 0 [1,2,3,4,5,6] ...



shaft utilization:

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

s=7:
period = 7; pre-periodic length = 0 [1,2,3,4,5,6,7] ...



shaft utilization:

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

s=8:
period = 8; pre-periodic length = 0 [1,2,3,4,5,6,7,8] ...



shaft utilization:

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

s=9:
period = 9; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9] ...



shaft utilization:

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

s=10:
period = 10; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10] ...



shaft utilization:

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

s=11:
period = 11; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11] ...



shaft utilization:

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

s=12:
period = 12; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11,12] ...



shaft utilization:

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

s=13:
period = 13; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11,12,13] ...



shaft utilization:

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

s=14:
period = 14; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11,12,13,14] ...



shaft utilization:

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

s=15:
period = 15; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] ...



shaft utilization:

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

s=16:
period = 16; pre-periodic length = 0 [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] ...



shaft utilization:

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

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e-mail: ralph@cs.arizona.edu

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