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
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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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