Last modified Wednesday, December 15, 1999 5:35 pm

Vishwanath's "random" Fibonacci sequence (one of infintely many).

1,1,2,-1,3,4,-1,5,4,-1,3,4,7,-3,-10,-7,3,10,7,17,-24,41,-65,24,41,65,24,41,17,24,-41,17,
-58,75,133,58,191,-249,440,-689,-249,938,1187,249,-1436,-1187,-249,938,-689,-249,-440,
689,1129,1818,-2947,1129,1818,2947,-1129,-1818,689,2507,1818,4325,-6143,-1818,-4325,2507,
1818,-689,2507,3196,-5703,8899,3196,12095,15291,-27386,-42677,15291,-27386,12095,-39481,
51576,-91057,-142633,-233690,-376323,-142633,233690,376323,-610013,233690,-843703,
-610013,-233690,-843703,1077393,233690,843703,...

s=4:

no period detected

1,1,2,3,3,4,3,1,4,3,3,4,3,1,2,1,3,2,3,1,4,1,3,4,1,1,4,1,1,4,3,1,2,3,1,2,3,3,4,3,3,2,3,1,
4,1,3,2,3,3,4,1,1,2,1,1,2,3,3,2,1,3,2,1,1,2,3,3,2,3,3,4,1,3,4,3,3,2,3,3,2,3,3,4,3,3,2,1,
3,2,3,3,2,1,3,2,1,1,2,3,...

shaft utilization:

    1:  27%  +++++++++++++++++++++++++++
    2:  20%  ++++++++++++++++++++
    3:  40%  ++++++++++++++++++++++++++++++++++++++++
    4:  13%  +++++++++++++

s=5:

no period detected

1,1,2,4,3,4,4,5,4,4,3,4,2,2,5,3,3,5,2,2,1,1,5,4,1,5,4,1,2,4,4,2,2,5,3,3,1,1,5,1,1,3,2,4,
4,3,1,3,1,1,5,4,4,3,3,4,3,2,1,2,4,2,3,5,2,2,5,2,3,1,2,1,2,4,1,5,1,4,3,1,4,5,4,1,3,2,5,2,
2,5,3,2,5,2,2,5,2,3,5,3,...

shaft utilization:

    1:  20%  ++++++++++++++++++++
    2:  24%  ++++++++++++++++++++++++
    3:  19%  +++++++++++++++++++
    4:  20%  ++++++++++++++++++++
    5:  17%  +++++++++++++++++

s=6:

no period detected

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

shaft utilization:

    1:  21%  +++++++++++++++++++++
    2:   9%  +++++++++
    3:  16%  ++++++++++++++++
    4:  13%  +++++++++++++
    5:  30%  ++++++++++++++++++++++++++++++
    6:  11%  +++++++++++

s=7:

no period detected

1,1,2,6,3,4,6,5,4,6,3,4,7,4,4,7,3,3,7,3,4,6,5,3,6,2,3,6,3,3,1,3,5,5,7,2,2,3,6,4,3,7,4,4,
6,3,3,7,4,3,1,3,2,5,7,2,5,7,5,2,3,1,5,6,3,2,1,1,5,4,1,4,2,2,4,6,3,5,2,3,5,6,6,7,6,6,5,4,
6,2,3,2,2,7,2,5,7,2,2,7,...

shaft utilization:

    1:   8%  ++++++++
    2:  17%  +++++++++++++++++
    3:  21%  +++++++++++++++++++++
    4:  14%  ++++++++++++++
    5:  13%  +++++++++++++
    6:  15%  +++++++++++++++
    7:  12%  ++++++++++++

s=8:

no period detected

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

shaft utilization:

    1:  20%  ++++++++++++++++++++
    2:  12%  ++++++++++++
    3:  17%  +++++++++++++++++
    4:   6%  ++++++
    5:   7%  +++++++
    6:   8%  ++++++++
    7:  23%  +++++++++++++++++++++++
    8:   7%  +++++++

s=9:

no period detected

1,1,2,8,3,4,8,5,4,8,3,4,7,6,8,2,3,1,7,8,3,5,7,6,5,2,6,5,8,6,4,8,5,3,7,4,2,3,8,4,3,2,8,6,
4,1,3,2,4,3,1,5,4,9,5,4,9,4,5,9,5,5,9,5,4,9,4,5,9,4,5,1,3,7,1,8,9,1,1,9,1,8,2,6,5,8,4,3,
8,5,6,7,5,2,7,4,2,3,5,7,...

shaft utilization:

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

s=10:

no period detected

1,1,2,9,3,4,9,5,4,9,3,4,7,7,10,3,3,10,7,7,6,1,5,4,1,5,4,1,7,4,9,7,2,5,3,8,1,1,10,1,1,8,7,
9,4,3,1,8,1,1,10,9,9,8,3,9,8,7,1,2,9,7,8,5,7,2,5,7,8,1,7,6,7,9,6,5,1,4,3,1,4,5,9,6,3,7,
10,7,7,10,3,7,10,7,7,10,7,3,10,3,...

shaft utilization:

    1:  16%  ++++++++++++++++
    2:   4%  ++++
    3:  12%  ++++++++++++
    4:   9%  +++++++++
    5:   8%  ++++++++
    6:   4%  ++++
    7:  20%  ++++++++++++++++++++
    8:   7%  +++++++
    9:  11%  +++++++++++
   10:   9%  +++++++++

s=11:

no period detected

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

shaft utilization:

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

s=12:

no period detected

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

shaft utilization:

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

s=13:

no period detected

1,1,2,12,3,4,12,5,4,12,3,4,7,10,3,6,3,10,7,4,2,2,13,11,2,13,11,2,4,11,11,4,7,10,3,6,9,11,
11,13,11,2,4,2,7,9,11,2,13,11,2,13,11,11,4,11,11,9,2,2,13,11,11,9,6,2,4,11,11,13,11,11,4,
7,11,5,3,5,2,3,5,5,13,5,8,3,11,1,3,2,12,12,2,10,12,11,10,5,2,3,...

shaft utilization:

    1:   3%  +++
    2:  16%  ++++++++++++++++
    3:  10%  ++++++++++
    4:  10%  ++++++++++
    5:   7%  +++++++
    6:   3%  +++
    7:   5%  +++++
    8:   1%  +
    9:   4%  ++++
   10:   5%  +++++
   11:  22%  ++++++++++++++++++++++
   12:   6%  ++++++
   13:   8%  ++++++++

s=14:

no period detected

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

shaft utilization:

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

s=15:

no period detected

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

shaft utilization:

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

s=16:

no period detected

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

shaft utilization:

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

e-mail: ralph@cs.arizona.edu

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