For 10 points, name this unsolved mathematical conjecture which states that any positive integer n will approach one after undergoing the iteration n over two if n is even or three n plus one
A proof that the set of integers under a certain stopping time has a limiting density is important in analyzing this problem. That proof was introduced by Riho Terras, whose notable modification of this problem introduces a one-half term and yields similar results. Sometimes associated with Helmut Hasse, it was the subject of Paul Erdos's quote that "mathematics is not yet ready for such problems." In 2008, Tomàs Oliveira e Silva expanded on earlier work by showing that this problem holds for all positive integers up to 5.48 times 10 to the 18th power. At least one of four cycles occur when negative numbers are introduced, while the sequence 4, 2, 1 always appears at end of the "hailstone" numbers, the sequence of numbers produced when this problem is applied to a positive integer. For 10 points, name this unsolved mathematical conjecture which states that any positive integer n will approach one after undergoing the iteration n over two if n is even or three n plus one if n is odd.
A proof that the set of integers under a certain stopping time has a limiting density is important in analyzing this problem.
{Collatz} conjecture or problem [or {Ulam's} conjecture or {Kakutani's} problem or the {Syracuse} problem or {Thwaites} conjecture; accept {3n} + {1 conjecture} or {problem} or {Hasse's conjecture} before mention; prompt on {hailstone problem} before mention]