2012/05/01 by Joshua Ide, Marc S. Renault, Marc Renault
Physics and Astronomy · Mathematics · Biochemistry, Genetics and Molecular Biology · #Advanced Mathematical Theories and Applications #Advanced Mathematical Theories #Fractal and DNA sequence analysis
paper · doi:10.1080/00150517.2012.12428012
We examine integer sequences G satisfying the Fibonacci recurrence relation Gn = Gn−1 + Gn−2 that also have the property G ≡ 1, a, a2, a3, … (mod m) for some modulus m. We determine those moduli m for which these power Fibonacci sequences exist and the number of such sequences for a given m. We also provide formulas for the periods of these sequences, based on the period of the Fibonacci sequence F modulo m. Finally, we establish certain sequence/subsequence relationships between power Fibonacci sequences.