UO-Sigma

[y.kohmoto]

    Hugo wrote :
    >Yasutoshi, SeqFans,

    >I may have a bad taste, but if we follow your suggestion than we can
find
    >zillions of (interesting??) sequences involving some real
    >parameter, maybe of the form integer + small eps.

    I mean that sequences which have a long boring part are not fit to OEIS.
    So, we might miss them.

    This property has no relationship with real parameter.

    Why do you say the form integer + small eps?
    Is there any interesting problem with the form?

    >What is so special about 0.00014? Why not 0.000141516171819?

    2.00014 is a representative of 2.00014 +/- eps.


    The case : a(n)=[1.5*a(n-1)+1]/2^r is the same sequence as Collatz's
3x+1 sequence.
    Because,   a(n)=(1.5*a(n-1)+0.5)/2^r=(3*a(n-1)+1)/2^(r-1) , this is the
definition of 3x+1 sequence.

    I wonder why mathematicians who research 3x+1 sequence study only one
point on all real numbers.
    I think that at least two sequences [1.4*a(n-1)+1]/2^r and
[1.6*a(n-1)+1.1]/2^r should be added on OEIS.
    The first sequence becomes periodic.
    5,7,5,7,.... or 29,41,29,41,.... or 33,47,33,47,.... etc
    The second sequence is still unknown.
    Don Reble calculated x(2,000,000) = 852756...564079; it has 46892digits,
where a(1) is 107.

    Minossi proved the analog of 3x+1 conjecture for the sequence
[2^(1/2)*a(n-1)+1]/2^r.
    Collatz's sequence exists on  a critical point between 1.4 and 1.6.

    Yasutoshi