051014 Fri 1830 Novato, CA rev. 051015 Sat 1750 (c) 2005 by Walter Bloch THREE RELATED LEXICAL PROBLEMS IN RETRIEVING DATA 1) HOW CAN YOU GOOGLE WHEN YOU DON’T HAVE A SEARCH KEY? Consider the following (famous) algorithm A applying to positive integers n: A[n]: if n = 1 then terminate; If n is even, then A[n/2]; otherwise A[3n+1]. For any n, there are three possibilities: The sequence terminates, e.g.: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The sequence repeats a number and loops forever. The sequence is nonterminating and nonrepeating, and so is unbounded, since under a ceiling a repeat is inevitable. For any n, in fact, the sequence terminates; last time I checked, this was unprovable. How can I google to check for progress, when I have forgotten the name of the sequence? Update: This example is from life; it inspired me to think about this and the related questions. It illustrates the point well enough, but it is not a perfect example, as it turn...