Generalized Go Sequence

[koh]

    Hi, Neil Seqfans.
    I generalized the sequence which appears in the formula of GO sequence.

    The original rule is the following :

    If b(n-1) is    divisible by two then b(n) = b(n-1)/2.
    If b(n-1) isn't divisible by two then b(n) = b(0)-(b(n-1)+1)/2.

    Generalized one is :

    If b(n-1) is    divisible by two then b(n) = b(n-1)/2.
    If b(n-1) isn't divisible by two then b(n) = k-(b(n-1)+1)/2.
         Where k is an integer which is not necessary b(0).

    [Example]
    k=47 

    1000,500,250,125,-16,-8,-4,-2,-1,47,23,35,29,32,16,8,4,2,1,46,23,....

    43,25,34,17,38,19,37,28,14,7,43,....

    41,26,13,40.20,10,5,44,22,11,41,....

    39,27,33,30,15,39,....

    31,31,....

    21,36,18,9,42,21,....

    3,45,24,12,6,3,....

    7 cycles exist.   



    %I A000001
    %S A000001 1000,500,250,125,-16,-8,-4,-2,-1,47,23,35,29,32,16,8,4,2,1,46,23,....
    %N A000001 Rule : If b(n-1) is divisible by two then b(n) = b(n-1)/2.
    If b(n-1) isn't divisible by two then b(n) = k-(b(n-1)+1)/2. b(0)=1000. k=47.
    %C A000001 For all integers i,j If k=i, b(0)=j then b(n) becomes periodic.             
    %Y A000001 A000002
    %K A000001 none
    %O A000001 1,1
    %A A000001 Yasutoshi Kohmoto   zbi74583 at boat.zero.ad.jp

  

    %I A000002
    %S A000002 1,1,1,1,2,1,1,3,2,1,3,1    
    %N A000002 Generate a sequence by the following rule.
               If b(n-1) is    divisible by two then b(n) = b(n-1)/2.
               If b(n-1) isn't divisible by two then b(n) = k-(b(n-1)+1)/2.
               Sequence gives number of cycles for each k.              
    %e A000002 k=11
               11,5,8,4,2,1,10,5,....
               9,6,3,9,....
               7,7,....
               Three cycles exist. So, a(11)=3
    %Y A000002 A000001
    %K A000002 none
    %O A000002 1,5
    %A A000002 Yasutoshi Kohmoto   zbi74583 at boat.zero.ad.jp




    Yasutoshi