Everest, Graham; Ward, Thomas Primes in divisibility sequences. (English) Zbl 1082.11004 Cubo Mat. Educ. 3, No. 2, 245-259 (2001). This very instructive survey elegantly introduces its various concepts and instructively links heuristics for the appearance of primes in the Fibonacci sequence, the Mersenne sequence, Lehmer- Pierce sequences and Elliptic divisibility sequences with the notion realizable sequence, to wit a sequence \((a_{n})\) counting the number \(a_{n}\) of periodic points of exact order \(n\) of some map \(T:X\to X\) on some set \(X\). Reviewer: Alf van der Poorten (Killara) Cited in 1 ReviewCited in 1 Document MSC: 11A41 Primes PDFBibTeX XMLCite \textit{G. Everest} and \textit{T. Ward}, Cubo Mat. Educ. 3, No. 2, 245--259 (2001; Zbl 1082.11004) Online Encyclopedia of Integer Sequences: The periodic point counting sequence for the toral automorphism given by the polynomial of (conjectural) smallest Mahler measure. The map is x -> Ax mod 1 for x in [0,1)^10, where A is the companion matrix for the polynomial x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1. Number of orbits of length n in map whose periodic points are A059928. A divisibility sequence derived from Lehmer’s polynomial x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1. Square root of the terms in A059928.