Select Page

Numberphile maintains an interesting collection of youtube videos. We will watch one in Math Seminar on February 9, 2022.

It is a tribute to J H Conway in the form of a podcast with animations.

J. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985) 3–23.

The Collatz Problem: If n is even, divide it by two. If n is odd, triple it and add one.

J. H. Conway, Unpredictable iterations, Proc. 1972 Number Theory Conference, Boulder (1972) 49–52.
It is reprinted in 2010 book by Lagarias
With p > 1 fixed, Conway considers the generalization $g(n) = a_i n + b_i$ where i = n mod p, and
$a_0, b_0, \ldots , a_{p-1}, b_{p-1}$ are rational constants chosen such that g(n) is always integral.
Conway proves that it is undecidable whether given a function g and positive integer n such
that g(n)/n is periodic there exists an integer k such that the k-fold iterate $g^k(n) = 1$.