Last modified Tuesday, January 11, 2000 5:04 pm

Perrin's sequence.

0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486,644,853,1130,1497,1983,
2627,3480,4610,6107,8090,10717,14197,18807,24914,33004,43721,57918,76725,101639,134643,
178364,236282,313007,414646,549289,727653,963935,1276942,1691588,2240877,2968530,3932465,
5209407,6900995,9141872,12110402,16042867,21252274,28153269,37295141,49405543,65448410,
86700684,114853953,152149094,201554637,267003047,353703731,468557684,620706778,822261415,
1089264462,1442968193,1911525877,2532232655,3354494070,4443758532,5886726725,7798252602,
10330485257,13684979327,18128737859,24015464584,31813717186,42144202443,55829181770,
73957919629,97973384213,129787101399,171931303842,227760485612,301718405241,399691789454,
529478890853,701410194695,929170680307,1230889085548,1630580875002,...

s=4:
period = 14; pre-periodic length = 0 [4,2,3,2,1,1,3,2,4,1,2,1,3,3] ...



shaft utilization:

    1:  28%  ++++++++++++++++++++++++++++
    2:  29%  +++++++++++++++++++++++++++++
    3:  28%  ++++++++++++++++++++++++++++
    4:  15%  +++++++++++++++

s=5:
period = 24; pre-periodic length = 0 [5,2,3,2,5,5,2,5,2,2,2,4,4,1,3,5,4,3,4,2,2,1,4,3] ...



shaft utilization:

    1:   8%  ++++++++
    2:  34%  ++++++++++++++++++++++++++++++++++
    3:  17%  +++++++++++++++++
    4:  20%  ++++++++++++++++++++
    5:  21%  +++++++++++++++++++++

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



shaft utilization:

    1:  13%  +++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  17%  +++++++++++++++++
    4:  10%  ++++++++++
    5:  26%  ++++++++++++++++++++++++++
    6:  14%  ++++++++++++++

s=7:
period = 48; pre-periodic length = 0 [7,2,3,2,5,5,7,3,5,3,1,1,4,2,5,6,7,4,6,4,3,3,7,6,3,6,2,2,1,4,3,5,7,1,5,1,6,6,7,5,6,5,4,4, 2,1,6,3] ...



shaft utilization:

    1:  12%  ++++++++++++
    2:  14%  ++++++++++++++
    3:  17%  +++++++++++++++++
    4:  12%  ++++++++++++
    5:  16%  ++++++++++++++++
    6:  16%  ++++++++++++++++
    7:  13%  +++++++++++++

s=8:
period = 28; pre-periodic length = 0 [8,2,3,2,5,5,7,2,4,1,6,5,7,3,4,2,7,6,1,5,7,6,4,5,2,1,7,3] ...



shaft utilization:

    1:  10%  ++++++++++
    2:  19%  +++++++++++++++++++
    3:  11%  +++++++++++
    4:  11%  +++++++++++
    5:  18%  ++++++++++++++++++
    6:  10%  ++++++++++
    7:  17%  +++++++++++++++++
    8:   4%  ++++

s=9:
period = 39; pre-periodic length = 0 [9,2,3,2,5,5,7,1,3,8,4,2,3,6,5,9,2,5,2,7,7,9,5,7,5,3,3,8,6,2,5,8,7,4,6,2,1,8,3] ...



shaft utilization:

    1:   5%  +++++
    2:  19%  +++++++++++++++++++
    3:  15%  +++++++++++++++
    4:   5%  +++++
    5:  18%  ++++++++++++++++++
    6:   7%  +++++++
    7:  13%  +++++++++++++
    8:   9%  +++++++++
    9:   9%  +++++++++

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



shaft utilization:

    1:   5%  +++++
    2:  14%  ++++++++++++++
    3:  11%  +++++++++++
    4:  10%  ++++++++++
    5:  10%  ++++++++++
    6:   3%  +++
    7:  20%  ++++++++++++++++++++
    8:   6%  ++++++
    9:  10%  ++++++++++
   10:  11%  +++++++++++

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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



shaft utilization:

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

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e-mail: ralph@cs.arizona.edu

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