Contents
Foreword
Preface
Acknowledgments
List of Figures
List of Tables
Chapter 1
Introduction
1.1. What the Book Is About
1.2. How the Book Flows
1.3. Preliminary Remarks
Chapter 2
Fibonacci Numbers and Structure
2.1. Infinite Series and Modular Rings
2.2. Equations for Primes Obtained from Integer Structure
2.3. Integer Structure Analysis of Primes and Composites from Sums of Two Fourth Powers
2.4. Prime Distributions in Prime Rows of the Modular Ring Z4
2.5. The Right-End-Digit Structure of Powers in the Modular Ring Z4
Chapter 3
Fibonacci Numbers and Primes
3.1. Fibonacci Numbers with Prime Subscripts
3.2. Fibonacci Number Sums as Prime Indicators
3.3. Fibonacci Primes
3.4. An Infinite Primality Conjecture for Prime-Subscripted Fibonacci Numbers
3.5 Primes within Generalized Fibonacci Sequences
3.6. Fibonacci and Lucas Primes
3.7. Prime Sequences from an Extended Sophie Germain Model
Chapter 4
Fibonacci Numbers and the Golden Ratio Family
4.1. Primitive Pythagorean Triples and Generalized Fibonacci Sequences
4.2. The Decimal String of the Golden Ratio
4.3. The Golden Ratio Family and the Binet Equation
4.4 Some Characteristics of the Golden Ratio Family
4.5. The Collatz Conjecture
Chapter 5
Transcendental Numbers and Triangles
5.1. The Pascal–Fibonacci Numbers
5.2. The Structure of ‘Pi’
5.3. Pellian Sequence Relationships among π, e,
5.4. Extensions to the Zeckendorf Triangle
5.5. Some Compositions Associated with Arbitrary Order Linear Recursive Sequences
Chapter 6
Conclusion
6.1. Related Topics
6.2. Summary
6.3. Concluding Comments
Bibliography
Brief Biographies of Authors
Index
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