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math.NT2003
Approximate Squaring
J. C. Lagarias, N. J. A. Sloane
We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then e…
math.NT2003★ 26 cited
The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author)
Jeffrey C. Lagarias
The 3x+ 1 problem concerns iteration of the map on the integers given by T(n) = (3n+1)/2 if n is odd; T(n) = n/2 if n is even. The 3x+1 Conjecture asserts that for every positive i…