A086773 Decimal expansion of the continued fraction 1/(Pi+1/(Pi+1/(Pi+1/(Pi+...)))).

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

Offset: 0

Author

Cino Hilliard, Aug 03 2003

Keywords

• easy
• nonn
• cons

Comments

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

Solves log(x+Pi) = -log(x). This equation represents the first (by absolute value) self-intersection of the spiral defined by the polar equation r=log(theta), and this constant is the smaller value of theta in the self-intersection. - Jeremy Tan, Sep 03 2016

Examples

			1
------
Pi + 1
     ------
     Pi + 1
          --------
           Pi + ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A188722.

Programs

Mathematica

RealDigits[N[(Sqrt[Pi^2 + 4] - Pi)/2, 120]] // First (* Michael De Vlieger, Mar 31 2015 *)

PARI

default(realprecision, 2000); f(n) = s=0; for(x=1,n,s=s+Pi; s=1/s); print(s)

Formula

Equals (sqrt(Pi^2+4)-Pi)/2 = 0.2912995... . - R. J. Mathar, Sep 15 2012