A near noble number is a real number continued
fraction is periodic, and the periodic sequence of terms is composed of a string
of integer
(1)
This can be written in the form
(2)
which can be solved to give
(3)
where Fibonacci number .
Special cases include
See also Periodic Continued Fraction ,
Noble Number
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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. Schroeder, M. "Noble and Near Noble
Numbers." In Fractals,
Chaos, Power Laws: Minutes from an Infinite Paradise. Referenced on Wolfram|Alpha Near Noble Number
Cite this as:
Weisstein, Eric W. "Near Noble Number."
From MathWorld https://mathworld.wolfram.com/NearNobleNumber.html
Subject classifications
whose continued
fraction is periodic, and the periodic sequence of terms is composed of a string
of 
1s followed by an integer 
,
![nu_(p,n)=[0,1,1,...,1_()_(p-1),n^_].](/images/equations/NearNobleNumber/NumberedEquation1.svg)
![nu_(p,n)=[0,1,1,...,1_()_(p-1),n,nu_(p,n)^(-1)],](/images/equations/NearNobleNumber/NumberedEquation2.svg)
is a Fibonacci number.
