Solution Re: [math-fun] 1,2,3,5,18 puzzle

<< << Puzzle: What do the positive integers 1, 2, 3, 5, 18 have in common with each other, but with no other positive integer (conjecturally) ?

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Hint: These number are cycle lengths.

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The answer is: 1, 2, 3, 5, 18 are the cycle lengths of the 5 known (and conjecturally, only) cycles of the Collatz function f: Z -> Z when iterated, where f(n) is defined as f(n) = n/2 if n is even; f(n) = 3n+1 if n is odd. The cycles -- of lengths 1, 2, 3, 5, 18 -- are those containing 0, -1, 1, -5, -17, respectively. --Dan