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# We define a function such that , and if there exists an integer such that , then is defined and if is odd if is even. What is the smallest

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We define a function $$f(x)$$ such that $$f(11)=34$$, and if there exists an integer $$a$$ such that $$f(a)=b$$, then $$f(b)$$ is defined and $$f(b)=3b+1$$ if $$b$$ is odd $$f(b)=\frac{b}{2}$$ if $$b$$ is even. What is the smallest possible number of integers in the domain of $$f$$?

Apr 12, 2020

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The smallest number of integers in the domain of f is 22.

Apr 13, 2020
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That isn't correct

qwertyzz  Apr 13, 2020
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This relates to the Collatz conjecture.  For the specific numbers quoted there are 15 different integers involved (that is, if I've interpreted the question correctly!), namely: 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

Apr 13, 2020