How many different holding patterns the sequence

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Question: Generate a program to test generalized hailstone numbers where xn = axn-1 +b if xn-1 is odd and xn = xn-1/2 if xn-1 is even where a and b are positive integers. For each of the a, b pairs less than or equal to 10, find whether or not the sequence seems to converge. Once you can do that, tell me how many different holding patterns the sequence converges to. For instance, when a = 3 and b = 5 then 1 ! 8 ! 4 ! 2 ! 1 this is holding pattern. However, if we start with a different number, say 5 we get a different holding pattern

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