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Date: 16-9-2020
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Date: 23-8-2020
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Date: 17-11-2019
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A near noble number is a real number whose continued fraction is periodic, and the periodic sequence of terms is composed of a string of 1s followed by an integer ,
(1) |
This can be written in the form
(2) |
which can be solved to give
(3) |
where is a Fibonacci number.
Special cases include
(4) |
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(5) |
REFERENCES:
Schroeder, M. R. Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity, 2nd enl. ed., corr. printing. Berlin: Springer-Verlag, 1990.
Schroeder, M. "Noble and Near Noble Numbers." In Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, pp. 392-394, 1991.
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