### Generalized 3x+1 functions and trajectory frequencies (mod m)

We study a function T: ℤ→ℤ with d (> 1) branches, defined in terms of
d non-zero integers m_{0},...,m_{d-1} and
d integers X_{0},...,X_{d-1}.
Then T(x)=int(m_{i}x ⁄ d)+X_{i}, if x≡ i (mod d).

**Example**. The *3x+1* mapping T(x)=x ⁄ 2 if x is even, (3x+1) ⁄ 2 if x is odd, corresponds to m_{0}=1, m_{1}=3, x_{0}=0, x_{1}=1.

Starting in 1982, Tony Watts and I investigated the frequencies of occupation of congruence classes (mod M)

of trajectories arising from generalized 3x+1 functions. (See earlier 3x+1 interests)

Experimentally we observed that all trajectories exhibited a limiting frequency of occupation of congruence classes (mod M).

The present program prints these frequencies for the iterates x, T(x), T^{2}(x), ...,T^{k-1}(x)

*Last modified 13th April 2010*

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