On ψ-function and two 2-Fibonacci sequences

Krassimir Atanassov, Dimitar Dimitrov and Anthony Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 16, 2010, Number 1, Pages 5—48
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Authors and affiliations

Krassimir Atanassov
CLBME – Bulgarian Academy of Sciences
P.O.Box 12, Sofia-1113, Bulgaria

Dimitar Dimitrov
CLBME – Bulgarian Academy of Sciences
P.O.Box 12, Sofia-1113, Bulgaria

Abstract

It is shown that the two essential 2-Fibonacci sequences have bases with respect to function ψ with length 24 and their extensions have bases with respect to function ψ with length 216.

Keywords

  • Fibonacci sequence
  • ψ-function

AMS Classification

  • 11B39

References

  1. Atanassov, K. An arithmetic function and some of its applications. Bull. of Number Theory and Related Topics, Vol. IX (1985), No. 1, 18-27.
  2. Atanassov K., L. Atanassova, D. Sasselov, A new perspective to the generalization of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 23 (1985), No. 1, 21-28.
  3. Atanassov K., On a second new generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 24 (1986), No. 4, 362-365.
  4. Lee J.-Z., J.-S. Lee, Some properties of the generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 25 (1987) No. 2, 111-117.
  5. Shannon A., R. Melham, Carlitz generalizations of Lucas and Lehmer sequences, The Fibonacci Quartarly, Vol. 31 (1993), No. 2, 105-111.

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Cite this paper

APA

Atanassov, K., & Dimitrov, D. (2010). On ψ-function and two 2-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 16(1), 5-48.

Chicago

Atanassov, Krassimir, and Dimitar Dimitrov. “On ψ-function and Two 2-Fibonacci Sequences.” Notes on Number Theory and Discrete Mathematics 16, no. 1 (2010): 5-48.

MLA

Atanassov, Krassimir, and Dimitar Dimitrov. “On ψ-function and Two 2-Fibonacci Sequences.” Notes on Number Theory and Discrete Mathematics 16.1 (2010): 5-48. Print.

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