A086775 Decimal expansion of the number defined by the continued fraction shown below.

4, 7, 7, 2, 5, 9, 9, 9, 6, 4, 7, 4, 0, 1, 9, 6, 4, 4, 5, 4, 2, 2, 2, 9, 8, 8, 4, 5, 0, 0, 6, 4, 4, 4, 6, 5, 4, 4, 6, 1, 0, 2, 3, 4, 7, 7, 6, 8, 0, 7, 4, 0, 3, 2, 2, 6, 9, 3, 2, 6, 9, 2, 3, 9, 4, 9, 2, 7, 7, 3, 8, 7, 9, 4, 5, 0, 7, 6, 1, 6, 4, 0, 4, 4, 9, 7, 6, 4, 1, 0, 1, 1, 8, 0, 8, 0, 2, 1, 5, 7, 2, 7, 6, 8, 7

Offset: 0

Author

Cino Hilliard, Aug 03 2003

Keywords

• easy
• nonn
• cons

Comments

This number is the inverse of the number whose decimal expansion is A136319. It is also the latter number minus phi. - Geoffrey Caveney, Apr 18 2014

Examples

			1
------
phi + 1
.... ------
.... phi + 1
......... -------
......... phi + etc
Equals 0.477259996...
		

Programs

PARI

?\p 2000 ?f(n) = phi=(sqrt(5)+1)/2; s=0; for(x=1,n,s=s+phi; s=1/s); print(s)

Formula

Repeat s = s + phi; s=1/s. The initial value of s is irrelevant.

Equals (sqrt(5+phi)-phi)/2, where phi = A001622. - R. J. Mathar, Sep 15 2012