Sequential Experiments with Primes

1. Front Matter

   Pages i-xi

   PDF

2. Introduction

   • Mihai Caragiu

   Pages 1-11

3. Warming Up: Integers, Sequences, and Experimental Mathematics

   • Mihai Caragiu

   Pages 13-65

4. Greatest Prime Factor Sequences

   • Mihai Caragiu

   Pages 67-149

5. Conway’s Subprime Function and Related Structures with a Touch of Fibonacci Flavor

   • Mihai Caragiu

   Pages 151-183

6. Going All Experimental: More Games and Applications

   • Mihai Caragiu

   Pages 185-247

7. Back Matter

   Pages 249-279

   PDF

With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions. Chapters include new mathematical ideas and open problems, some of which are proved in the text. Vector valued MGPF sequences, extensions of Conway’s Subprime Fibonacci sequences, and linear complexity of bit streams derived from GPF sequences are among the topics covered in this book. This book is perfect for the pure-mathematics-minded educator in a small undergraduate college as well as graduate students and advanced undergraduate students looking for a significant high-impact learning experience in mathematics.

• Computational Number Theory
• Prime Numbers
• Cryptography
• Ducci Game
• Fibonacci Sequences
• GPF Sequences

“Caragiu (Ohio Northern Univ.) offers readers a valuable case study in fostering undergraduate research; he focuses on processes analogous to the Fibonacci sequence (generate each term by adding the previous two), twisted now by passing to the largest prime dividing the sum (or by dividing out the smallest prime). … Recommended. Undergraduates and above.” (D. V. Feldman, Choice, Vol. 56 (1), September, 2018)



“Caragiu’s book is a lovely synthesis of both ideas illustrated with sequences based on prime numbers. … this book offers you many ideas to explore and is an excellent foray into experimental mathematics. … Overall, this is an excellent book. If you are interested in experimental math and want to play, you’ll enjoy this book.” (David S. Mazel, MAA Reviews, December, 2017)

• Ohio Northern University , Ada, USA

  Mihai Caragiu

Mihai Caragiu is a professor of mathematics at Ohio Northern University. He is the recipient of the 2010 Outstanding Teaching Faculty Award for the Department of Mathematics and Statistics. 

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