The Pascal–Fibonacci numbers

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 3, Pages 5–11
Full paper (PDF, 131 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology Sydney
NSW 2007, Australia

Abstract

The Pascal–Fibonacci (PF) numbers for a given Fibonacci number sum to give the values of that Fibonacci number. Individual PF numbers are members of one of the triangular, tetrahedral or pentagonal series or have factors in common with the pyramidal or other geometric series. For composite numbers, partial sums of PF numbers can yield a factor, while prime Fibonacci numbers are detected with sums of squares.

Keywords

• Fibonacci numbers
• Binet equation
• Pascal Triangle
• Triangular numbers
• Tetrahedral numbers
• Pentagonal numbers
• Pyramidal numbers

AMS Classification

• 11B39
• 11B50

References

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