Coxeter, H. S. M. Cyclic sequences and frieze patterns. The Fourth Felix Behrend Memorial Lecture. (English) Zbl 1222.01047 Lagarias, Jeffrey C. (ed.), The ultimate challenge. The \(3x+1\) problem. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4940-8/hbk). 211-217 (2010). This paper is the written version of a 1970 lecture, which was published in 1971 in Vinculum 8, 4–7 (1971), the journal of the Mathematical Association of Victoria (Australia). It seems to be the earliest published paper that explicitly states the \(3x+1\) problem. It presents the problem at the end of the lecture as “mathematical gossip.” Coxeter offers a $50.00 prize for its solution. The main subject of the paper, cyclic sequences and frieze patterns, is of interest in its own right. The author refers to the life and work of Felix Adalbert Behrend (1911–1962).For the entire collection see [Zbl 1253.11003]. Reviewer: Florin Nicolae (Berlin) MSC: 11B83 Special sequences and polynomials 01A70 Biographies, obituaries, personalia, bibliographies Keywords:Memorial Lecture; Felix Adalbert Behrend; 3x+1 problem; frieze patterns Biographic References: Behrend, Felix Adalbert PDFBibTeX XMLCite \textit{H. S. M. Coxeter}, in: The ultimate challenge. The \(3x+1\) problem. Providence, RI: American Mathematical Society (AMS). 211--217 (2010; Zbl 1222.01047)