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

The 11-sided poylgonal numbers.

1,11,30,58,95,141,196,260,333,415,506,606,715,833,960,1096,1241,1395,1558,1730,1911,2101,
2300,2508,2725,2951,3186,3430,3683,3945,4216,4496,4785,5083,5390,5706,6031,6365,6708,
7060,7421,7791,8170,8558,8955,9361,9776,10200,10633,11075,11526,11986,12455,12933,13420,
13916,14421,14935,15458,15990,16531,17081,17640,18208,18785,19371,19966,20570,21183,
21805,22436,23076,23725,24383,25050,25726,26411,27105,27808,28520,29241,29971,30710,
31458,32215,32981,33756,34540,35333,36135,36946,37766,38595,39433,40280,41136,42001,
42875,43758,44650,...

s=4:

period = 8; pre-periodic length = 0

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

shaft utilization:

    1:  25%  +++++++++++++++++++++++++
    2:  26%  ++++++++++++++++++++++++++
    3:  25%  +++++++++++++++++++++++++
    4:  24%  ++++++++++++++++++++++++

s=5:

period = 5; pre-periodic length = 0

[1,1,5,3,5] ...

shaft utilization:

    1:  40%  ++++++++++++++++++++++++++++++++++++++++
    2:   0%  
    3:  20%  ++++++++++++++++++++
    4:   0%  
    5:  40%  ++++++++++++++++++++++++++++++++++++++++

s=6:

period = 12; pre-periodic length = 0

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

shaft utilization:

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

s=7:

period = 7; pre-periodic length = 0

[1,4,2,2,4,1,7] ...

shaft utilization:

    1:  29%  +++++++++++++++++++++++++++++
    2:  28%  ++++++++++++++++++++++++++++
    3:   0%  
    4:  29%  +++++++++++++++++++++++++++++
    5:   0%  
    6:   0%  
    7:  14%  ++++++++++++++

s=8:

period = 16; pre-periodic length = 0

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

shaft utilization:

    1:  13%  +++++++++++++
    2:  13%  +++++++++++++
    3:  13%  +++++++++++++
    4:  12%  ++++++++++++
    5:  12%  ++++++++++++
    6:  13%  +++++++++++++
    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 = 20; pre-periodic length = 0

[1,1,10,8,5,1,6,10,3,5,6,6,5,3,10,6,1,5,8,10] ...

shaft utilization:

    1:  20%  ++++++++++++++++++++
    2:   0%  
    3:  10%  ++++++++++
    4:   0%  
    5:  20%  ++++++++++++++++++++
    6:  20%  ++++++++++++++++++++
    7:   0%  
    8:  10%  ++++++++++
    9:   0%  
   10:  20%  ++++++++++++++++++++

s=11:

period = 11; pre-periodic length = 0

[1,11,8,3,7,9,9,7,3,8,11] ...

shaft utilization:

    1:  10%  ++++++++++
    2:   0%  
    3:  18%  ++++++++++++++++++
    4:   0%  
    5:   0%  
    6:   0%  
    7:  18%  ++++++++++++++++++
    8:  18%  ++++++++++++++++++
    9:  18%  ++++++++++++++++++
   10:   0%  
   11:  18%  ++++++++++++++++++

s=12:

period = 24; pre-periodic length = 0

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

shaft utilization:

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

s=13:

period = 13; pre-periodic length = 0

[1,11,4,6,4,11,1,13,8,12,12,8,13] ...

shaft utilization:

    1:  16%  ++++++++++++++++
    2:   0%  
    3:   0%  
    4:  16%  ++++++++++++++++
    5:   0%  
    6:   8%  ++++++++
    7:   0%  
    8:  15%  +++++++++++++++
    9:   0%  
   10:   0%  
   11:  16%  ++++++++++++++++
   12:  14%  ++++++++++++++
   13:  15%  +++++++++++++++

s=14:

period = 28; pre-periodic length = 0

[1,11,2,2,11,1,14,8,11,9,2,4,1,7,8,4,9,9,4,8,7,1,4,2,9,11,8,14] ...

shaft utilization:

    1:  15%  +++++++++++++++
    2:  15%  +++++++++++++++
    3:   0%  
    4:  14%  ++++++++++++++
    5:   0%  
    6:   0%  
    7:   7%  +++++++
    8:  14%  ++++++++++++++
    9:  13%  +++++++++++++
   10:   0%  
   11:  15%  +++++++++++++++
   12:   0%  
   13:   0%  
   14:   7%  +++++++

s=15:

period = 15; pre-periodic length = 0

[1,11,15,13,5,6,1,5,3,10,11,6,10,8,15] ...

shaft utilization:

    1:  14%  ++++++++++++++
    2:   0%  
    3:   7%  +++++++
    4:   0%  
    5:  14%  ++++++++++++++
    6:  13%  +++++++++++++
    7:   0%  
    8:   6%  ++++++
    9:   0%  
   10:  13%  +++++++++++++
   11:  13%  +++++++++++++
   12:   0%  
   13:   7%  +++++++
   14:   0%  
   15:  13%  +++++++++++++

s=16:

period = 32; pre-periodic length = 0

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

shaft utilization:

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

e-mail: ralph@cs.arizona.edu

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