Fibonacci numbers with prime subscripts: Digital sums for primes versus composites

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 3, Pages 45–49
Full paper (PDF, 190 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

If we use the expression F_p = kp ± 1, p prime, then digital sums of k reveal specific values for primes versus composites in the range 7 ≤ p ≤ 107. The associated digital sums of F_p±1 also yield prime/composite specificity. It is shown too that the first digit of F_p, and hence for the corresponding triples, (F_p, F_p±1) and (F_p, F_p−1, F_p−2) can be significant for primality checks.

Keywords

• Fibonacci numbers
• Primality
• Digit sums

AMS Classification

• 11B39
• 11B50

References

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