A270782 Sequence arising from a mixed continued fraction for Pi: Pi = 22/(7+1/(354+1/(1+1/(12+...)))).

354, 1, 12, 2, 1, 7, 2, 4, 3, 1, 6, 2, 2, 1, 1, 3, 7, 1, 1, 3, 2, 1, 37, 2, 3, 2, 1, 1, 1, 7, 19, 3, 1, 6, 1, 3, 1, 2, 54, 2, 15, 4, 1, 1, 2, 1, 3, 1, 33, 2, 15, 1, 4, 1, 1, 1, 1, 3, 41, 1, 1, 3, 3, 2, 1, 4, 4, 1, 9, 7, 2, 4, 1, 2, 23, 7, 3, 7, 1, 1, 20, 9, 7, 62, 1, 8, 24, 2, 3, 1, 1, 2, 1, 1, 3, 2

Offset

0,1

Comments

This is the continued fraction expansion of c = 22/Pi - 7.

Links

Table of n, a(n) for n=0..95.

J. W. Knoderer, Continuous Fractions converging on the value of pi, Mazes.com, 2016

J. W. Knoderer, Directions: How to calculate continuous fraction for Pi, Mazes.com, 2016.

J. W. Knoderer, Continuous Fraction for pi, 33 denominators

Example

The resulting successive approximations to Pi are:
Fraction 0: 22/7
Fraction 1: 22/(7+1/354)
Fraction 2: 22/(7+1/(354+1/1))
Fraction 3: 22/(7+1/(354+1/(1+1/12)))
To see fractions 4 to 35, see the links.

Maple

with(numtheory); Digits:=200:
c:=22/Pi - 7;
convert(evalf(c), confrac); # N. J. A. Sloane, Apr 05 2016

Crossrefs

Sequence in context: A213470 A068684 A377219 * A251127 A176197 A157668

Adjacent sequences: A270779 A270780 A270781 * A270783 A270784 A270785

Keyword

nonn,cofr

Author

John William Knoderer, Mar 22 2016

Extensions

Edited by N. J. A. Sloane, Apr 05 2016

Status

approved