Assume that the monster fraction shown below is a well-defined real number. Then it is a very familiar number. What is it?
1 + ... 1 + -------- 3 + ... 1 + ------------ 5 + ... 3 + -------- 1 + ... 1 + ---------------- 1 + ... 5 + -------- 3 + ... 3 + ------------ 5 + ... 1 + -------- 1 + ... 1 + -------------------- 1 + ... 1 + -------- 3 + ... 5 + ------------ 5 + ... 3 + -------- 1 + ... 3 + ---------------- 1 + ... 5 + -------- 3 + ... 1 + ------------ 5 + ... 1 + -------- 1 + ...The pattern is that the columns, from the top, come from:
1351 1351 1351 1351 ...
Source: Recent Crux Math., which refers to Mathematics and Informatics Quarterly 1/97 vol. 7, which refers to an original contribution by Edwin O. Buchman (Fullerton, CA) Jan/Feb 1996 Quantum (which has 3 such weird continued things). © Copyright 1998 Stan Wagon. Reproduced with permission.