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

The Fibonacci sequence.

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,
46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,
14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,
1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,
32951280099,53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,
956722026041,1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,
17167680177565,27777890035288,44945570212853,72723460248141,117669030460994,
190392490709135,308061521170129,498454011879264,806515533049393,1304969544928657,
2111485077978050,3416454622906707,5527939700884757,8944394323791464,14472334024676221,
23416728348467685,37889062373143906,61305790721611591,99194853094755497,
160500643816367088,259695496911122585,420196140727489673,679891637638612258,
1100087778366101931,1779979416004714189,2880067194370816120,4660046610375530309,
7540113804746346429,12200160415121876738,19740274219868223167,31940434634990099905,
51680708854858323072,83621143489848422977,135301852344706746049,218922995834555169026,
354224848179261915075,...

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



shaft utilization:

    1:  50%  ++++++++++++++++++++++++++++++++++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:  17%  +++++++++++++++++
    4:  16%  ++++++++++++++++

s=5:
period = 20; pre-periodic length = 0 [1,1,2,3,5,3,3,1,4,5,4,4,3,2,5,2,2,4,1,5] ...



shaft utilization:

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

s=6:
period = 24; pre-periodic length = 0 [1,1,2,3,5,2,1,3,4,1,5,6,5,5,4,3,1,4,5,3,2,5,1,6] ...



shaft utilization:

    1:  26%  ++++++++++++++++++++++++++
    2:  13%  +++++++++++++
    3:  17%  +++++++++++++++++
    4:  12%  ++++++++++++
    5:  24%  ++++++++++++++++++++++++
    6:   8%  ++++++++

s=7:
period = 16; pre-periodic length = 0 [1,1,2,3,5,1,6,7,6,6,5,4,2,6,1,7] ...



shaft utilization:

    1:  26%  ++++++++++++++++++++++++++
    2:  13%  +++++++++++++
    3:   7%  +++++++
    4:   6%  ++++++
    5:  12%  ++++++++++++
    6:  24%  ++++++++++++++++++++++++
    7:  12%  ++++++++++++

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



shaft utilization:

    1:  26%  ++++++++++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:   9%  +++++++++
    4:   0%  
    5:  24%  ++++++++++++++++++++++++
    6:   0%  
    7:   8%  ++++++++
    8:  16%  ++++++++++++++++

s=9:
period = 24; pre-periodic length = 0 [1,1,2,3,5,8,4,3,7,1,8,9,8,8,7,6,4,1,5,6,2,8,1,9] ...



shaft utilization:

    1:  22%  ++++++++++++++++++++++
    2:   9%  +++++++++
    3:   9%  +++++++++
    4:   8%  ++++++++
    5:   8%  ++++++++
    6:   8%  ++++++++
    7:   8%  ++++++++
    8:  20%  ++++++++++++++++++++
    9:   8%  ++++++++

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



shaft utilization:

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

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



shaft utilization:

    1:  30%  ++++++++++++++++++++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  10%  ++++++++++
    4:   0%  
    5:  10%  ++++++++++
    6:   0%  
    7:   0%  
    8:  10%  ++++++++++
    9:   0%  
   10:  10%  ++++++++++
   11:  10%  ++++++++++

s=12:
period = 24; pre-periodic length = 0 [1,1,2,3,5,8,1,9,10,7,5,12,5,5,10,3,1,4,5,9,2,11,1,12] ...



shaft utilization:

    1:  22%  ++++++++++++++++++++++
    2:   9%  +++++++++
    3:   9%  +++++++++
    4:   4%  ++++
    5:  20%  ++++++++++++++++++++
    6:   0%  
    7:   4%  ++++
    8:   4%  ++++
    9:   8%  ++++++++
   10:   8%  ++++++++
   11:   4%  ++++
   12:   8%  ++++++++

s=13:
period = 28; pre-periodic length = 0 [1,1,2,3,5,8,13,8,8,3,11,1,12,13,12,12,11,10,8,5,13,5,5,10,2,12,1,13] ...



shaft utilization:

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

s=14:
period = 48; pre-periodic length = 0 [1,1,2,3,5,8,13,7,6,13,5,4,9,13,8,7,1,8,9,3,12,1,13,14,13,13,12,11,9,6,1,7,8,1,9,10,5,1, 6,7,13,6,5,11,2,13,1,14] ...



shaft utilization:

    1:  18%  ++++++++++++++++++
    2:   5%  +++++
    3:   5%  +++++
    4:   2%  ++
    5:   8%  ++++++++
    6:   8%  ++++++++
    7:   8%  ++++++++
    8:   8%  ++++++++
    9:   8%  ++++++++
   10:   2%  ++
   11:   4%  ++++
   12:   4%  ++++
   13:  16%  ++++++++++++++++
   14:   4%  ++++

s=15:
period = 40; pre-periodic length = 0 [1,1,2,3,5,8,13,6,4,10,14,9,8,2,10,12,7,4,11,15,11,11,7,3,10,13,8,6,14,5,4,9,13,7,5,12,2, 14,1,15] ...



shaft utilization:

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

s=16:
period = 24; pre-periodic length = 0 [1,1,2,3,5,8,13,5,2,7,9,16,9,9,2,11,13,8,5,13,2,15,1,16] ...



shaft utilization:

    1:  14%  ++++++++++++++
    2:  17%  +++++++++++++++++
    3:   5%  +++++
    4:   0%  
    5:  12%  ++++++++++++
    6:   0%  
    7:   4%  ++++
    8:   8%  ++++++++
    9:  12%  ++++++++++++
   10:   0%  
   11:   4%  ++++
   12:   0%  
   13:  12%  ++++++++++++
   14:   0%  
   15:   4%  ++++
   16:   8%  ++++++++

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e-mail: ralph@cs.arizona.edu

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