period

[y.kohmoto]

    Hello, seqfans.
    I conjectured that the following two sequences are cyclic.

    x(n)=[a*x(n-1)+b]/p^r,　 a, b are real number, [x] is integer part of x,
                        p is prime, p^r is the highest power of p dividing
[a*x(n-1)+b]

    seq.1.    x(0), p, a, b = 1, 2, 2.00013, 3.0
    seq.2.    x(0), p, a, b = 1, 2, 2.00001, 3.2

    My computer Pentium 366MHz is too slow to find these periods.
    If anyone has faster computer, please calculate the periods and tell me
them.

    Yasutoshi