My book The Perrin Chalkboard: New Insights into Integer Sequences is now available as an e-book. 
In 1899, a French engineer R. Perrin proposed in a brief query a recurrence sequence whose integer values are divisible by N only when N is prime.  The Perrin Chalkboard explores the question, “what can be learned by studying integer sequences”?  Sequences or “linear recurrences” are found in science, art, and music. A biologist studies sequences of amino acids and nucleic acids in proteins and DNA.  Are these sequences random or have they been created from a mathematically determined program?  Nature mimics patterns that follow a series of numbers such as found in the ancient marine ammonite or the spiral patterns of sunflowers.  Sequences are shown to be products of higher mathematical functions that can describe many physical phenomena.