Near Noble Number
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 
,
![nu_(p,n)=[0,1,1,...,1_()_(p-1),n^_].](https://mathworld.wolfram.com/images/equations/NearNobleNumber/NumberedEquation1.gif) |
(1)
|
This can be written in the form
![nu_(p,n)=[0,1,1,...,1_()_(p-1),n,nu_(p,n)^(-1)],](https://mathworld.wolfram.com/images/equations/NearNobleNumber/NumberedEquation2.gif) |
(2)
|
which can be solved to give
 |
(3)
|
where 
is a Fibonacci number.
Special cases include
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.
