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Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz

In: Applications of Fibonacci Numbers

Author

Listed:
  • Heiko Harborth
  • Silke Maasberg

Abstract

In every k-coloring of the first N natural numbers (k ≥ 2), does there exist a monochromatic s-term Fibonacci sequence (s ≥ 3), that is, a sequence f 1 ,f 2 ,…,f 8 where f n + 2 = f n + 1+ f n , n ≥ 1, and f1,f2 are arbitrary natural numbers? In case of existence, the smallest N with this property is called Rado number RaF(k,s) for Fibonacci sequences. For s = 3 the numbers RaF(k, 3) are known as Schur numbers [9]. A similar question for Rado numbers of second order linear recurrences was posed by S. Rabinowitz [12].

Suggested Citation

  • Heiko Harborth & Silke Maasberg, 1996. "Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 143-153, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0223-7_13
    DOI: 10.1007/978-94-009-0223-7_13
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