Smarandache sequences are a family of sequences of integers around which one can formulate various number-theoretical questions. For example, on page 6 of this book, we find the "Smarandache Symmetric Sequence",
followed by the question "How many primes are there in this sequence?".
Pluckings from the Tree of Smarandache Sequences and Functions is Charles Ashbacher's third book on "Smarandache Notions." In this book, he tries to make some progress on questions such as the one above, questions which are generally very difficult. Ashbacher plays with the various notions, obtains partial results, does computer experiments. There are a few theorems, but mostly there are questions, conjectures, and examples. Most of the mysteries being studied remain mysterious.
Fernando Gouvêa (email@example.com) is Associate Professor of Mathematics at Colby College in Waterville, Maine. His special interests include number theory, history of mathematics, science fiction, and Christian theology.