Kimyo-sequence

[y.kohmoto]

    Hello, seqfans.
    I give a table of periods for a(n)=[A*a(n-1)+B]/2^r , A=1.1 to 3.0 ,
B=0.5 to 1.4 , where 2^r is the highest power of 2 dividing [A*a(n-1)+B].
    Numbers mean periods and "oo" represents that the period is unknown.

                A=1.1+0.1*k    , k=0 to 29
    B   0.5       01 01 01 02 01 03 01 oo 01 01 01 oo 89 oo oo oo oo 02 oo
oo
         0.6       01 01 01 02 01 01 01 01 01 01 01 01 89 oo oo oo oo oo oo
oo
         0.7       01 01 01 02 01 01 01 01 01 01 01 01 oo oo oo oo oo oo oo
oo
         0.8       01 03 01 02 01 01 01 01 01 01 01 oo oo 02 oo oo oo oo oo
oo
         0.9       01 03 02 02 01 01 01 01 01 01 04 oo 04 02 oo oo oo oo oo
oo
         1.0       01 01 02 02 01 01 01 01 01 01 04 03 04 02 oo 05 oo oo oo
01
         1.1       05 01 02 02 01 oo 01 01 01 01 04 03 02 02 oo 05 60 oo oo
01
         1.2       05 01 02 02 01 07 01 01 01 01 04 oo 02 02 oo oo 60 02 oo
01
         1.3       01 01 02 02 01 07 01 01 01 01 03 oo oo 02 oo oo 01 02 oo
01
         1.4       01 04 02 02 01 07 01 07 01 01 03 02 oo 02 oo oo 01 oo oo
01


    The 5th column : A=1.1+0.1*4=1.5 and the 30th column : A=3.0 , 1.0<=B
correspond  Collatz's 3x+1 sequence.
    The calculations started at a(0) = 107 ,    naturally the periods become
1.

    These are an old results.
    I wonder if some of the periods are not correct, because a software
which I used might have an overflow.

    {A=1.6, B=1.1} is an unique point.
    >Don Reble calculated x(2,000,000) = 852756...564079; it has
46892digits,

    Between A=2.0 and A=2.1 , many strange sequences exist.
    See my home page. An image of Kimyo sequence exists.
    http://boat.zero.ad.jp/~zbi74583/another02.htm

    Yasutoshi