A189088 Decimal expansion of Pi - sqrt(Pi^2 - 1).

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

Offset

0,2

Comments

Decimal expansion of the shape (= length/width = Pi - sqrt(-1+Pi^2)) of the lesser 2*Pi-contraction rectangle.

See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for transcendental numbers

Example

0.1634045465204364424868140709760745094117386882...

Mathematica

r = 2*Pi; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]  (* A189088 *)
ContinuedFraction[t, 120]
RealDigits[Pi-Sqrt[Pi^2-1], 10, 150][[1]] (* Harvey P. Dale, Sep 25 2016 *)

Prog

(PARI) Pi*(1-sqrt(1-1/Pi^2)) \\ Charles R Greathouse IV, May 07 2011

Crossrefs

Cf. A188738, A189089, A189090.

Sequence in context: A108661 A117042 A227989 * A195301 A196824 A309988

Adjacent sequences: A189085 A189086 A189087 * A189089 A189090 A189091

Keyword

nonn,easy,cons

Author

Clark Kimberling, Apr 16 2011

Status

approved