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 ,

(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)
			(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.