Silver Constant

The silver constant is the algebraic number given by

			(1)
			(2)
			(3)

(OEIS A116425), where  denotes a polynomial root.

Defining the nested radical expression

(4)

the silver constant is given by

(5)

(T. Piezas, pers. comm., Feb. 16, 2006).

The silver constant is the seventh Beraha constant. Surprisingly, it also appears in the 3-cycle of the logistic map.

REFERENCES:

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, pp. 51 and 143, 1983.

Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, p. 162, 1986.

Sloane, N. J. A. Sequence A116425 in "The On-Line Encyclopedia of Integer Sequences."