논문KCI 등재
The digital root function for Fibonacci-type sequences
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The base of digit roots of elements of a sequence of numbers is defined, with examples given for the Fibonacci, Lucas, Lucas-Lehmer and Euler sequences. The theory is then applied to extensions of the Pell-Padovan and Tribonacci sequences.
Abstract
The base of digit roots of elements of a sequence of numbers is defined, with examples given for the Fibonacci, Lucas, Lucas-Lehmer and Euler sequences. The theory is then applied to extensions of the Pell-Padovan and Tribonacci sequences.
참고문헌 (8)
- Atanassov,K.T, "An arithmetic function and some of its applications", Bulletin of Number Theory and Related Topics, 9(1), pp.18~27 (1985)
- Atanassov K.T, "A digit sum arithmetical function", Bulletin of Number Theory and Related Topics, 11(1), pp.37~49 (1987)
- Dence,Joseph B, "Elements of the Theory of Numbers", pp.83~155 (1999), Academic Press
- Gardiner,A, "Digital Roots,Rings and Clock Arithmetic", The Mathematical Gazette, 66(437), pp.184~188 (1982)
- Shannon A.G, "Generalized staggered sums", The Fibonacci Quarterly, 29(1), pp.47~51 (1991)
- Shannon,A.G, "Some Properties of Generalized Third Order Pell Numbers", 2008. 13th International Conference on Fibonacci Numbers and Their Applications (2008), University of Patras
- Shannon,A.G, "The Auxiliary Equation Associated with the Plastic Number", Notes on Number Theory & Discrete Mathematics, 12(1), pp.1~12 (2006)
- Shannon, A.G, "Properties of Cordonnier, Perrin and Van der Laan Numbers", International Journal of Mathematical Education in Science & Technology, 37(7), pp.825~831
관련 논문AI추천
Generalized Fibonacci-Feinberg sequencesA.G. Shannon, C. K. Cook장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호A BASIC LINEAR RECURSIVE SEQUENCE OF ARBITRARY ORDERA. G. Shannon장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호On the sequences related to Fibonacci and Lucas numbersNihal Yilmaz Ä, OzgÄ, ur대한수학회 · 대한수학회지2005 · 제42권 제1호Generalized Padovan sequencesJhon J. Bravo, Jose L. Herrera대한수학회 · 대한수학회논문집2022 · 제37권 제4호Applications of Euler-Seidel matricesA. Dil, V. Kurt장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제18권 제2호On conditionally defined Fibonacci and Lucas sequences and periodicitySandra Spiroff, Skylyn Irby대한수학회 · 대한수학회보2020 · 제57권 제4호
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