Three periodic orbits in the 3x-1 iteration.
1, 5, 7, 10, 17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34
1
The iteration is: if x is even, then x/2, otherwise (3x-1)/2. The orbits, listed in the paper by Bell and Lagarias, are {1}, {5, 7, 10}, and {17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34}. Sequence S000240 applies the 3x-1 iteration to the odd numbers.
T. D. Noe, Plot of 15 terms
Jason P. Bell and Jeffrey C. Lagarias, 3x+1 inverse orbit generating functions almost always have natural boundaries, arXiv 1408.6884 (Aug 28 2014)
L. Berg and G. Opfer, An analytic approach to the Collatz 3n+1 problem for negative start values, Computational Methods and Function Theory, 13 (2013), 225–236.
Cf. A001281, A003124, S000240.
nonn
T. D. Noe, Sep 02 2014