Last week, I wrote about one of my more spectacular failures, which involved a progression that began 1, 2, 4, 8, 16, 32, but then rather than continuing sensibly as 64, 128, ..., instead exploded into 273, 65569, 4294967361, and 1.5x1082. The next term is a little over 265569 and the term after that a little over 24294967361, which has about a billion digits when written out in full.
