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# A Continued Monster

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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.