Collatz conjecture
Syracuse function

If k is an odd integer, then 3 k + 1 is even, so 3 k + 1 = 2 k ′ with k ′ odd and a ≥ 1. The Syracuse function is the function f from the set I of positive odd integers into itself, for which f (k) = k ′ (sequence A075677 in the OEIS).

Some properties of the Syracuse function are:

The Collatz conjecture is equivalent to the statement that, for all k in I, there exists an integer n ≥ 1 such that f (k) = 1.
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