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The Collatz problem could also be restated as asking whether the iterated reduced Collatz function R ( 2 n − 1 ) , n ≥ 1 , {\displaystyle \scriptstyle R(2n-1),\,n\,\geq \,1,\,} where R ( k ) = 3 k + 1 2 r , {\displaystyle \scriptstyle R(k)\,=\,{\frac {3k+1}{2^{r}}},\,} with r {\displaystyle \scriptstyle r\,} as large as possible, always reaches an even power of 2 (a power of 4), in which case the hailstone height then decreases exponentially down to 1.
A075677 Reduced Collatz function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (3k+1)/2^r, with r as large as possible.