[seqfan] RE : 8/5 Sequence

kohmoto zbi74583.boat at orange.zero.jp
Fri Jun 22 03:12:29 CEST 2012


    Thanks for Maximilian's explanation.
    I understood that A082010 is the map of 8/5 sequence.
    I had thought that it is the orbit of 0.

    Neil
    I think both your sequence  are correct.

    I found three 8/5 sequences which have long periods.

    S.1.
    a(n)=[A*a(n-1)+B]/2^n
    Where [M] is Integer part of M. 
                2^n is the highest two power dividing [A*a(n-1)+B]

    a(0)=7, A=1.6, B=1.00000001
    Period=5082

    S.2.
    a(0)=7, A=1.6, B=1.00000002
    Period=1664

    S.3.
    a(0)=7, A=1.6, B=1.00000003
    Period=107365

    The case of B=1.0, it is probably unlimited.
    Because Don Reble computed the 2000000th term and it has 46000 digits.         
    In this mail  8/5 sequence is represented as a K-Sequence.
    So periods become much shorter.

    I computed these three sequence using a program written in UBASIC.
    This language makes a mistake sometimes.
    Could anyone confirm these results?
    Could anyone also confirm Reble's result?
    I wonder if A152199 is limited or not. 



    Yasutoshi
    


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